(ア) f(x)=x^5+(a)x^4+(b)x^3+(c)x^2+(d)x+(e) (-10≦a,b,c,d≦10,1≦e≦10, a,b,c,d,eは整数)の内, 既約で可解な方程式の個数を SageMath で計算しました.計算時間は約30分でした. 結果は[[a,b,c,d,e], order] の形で出力してます.orderはGalois群Galの位数です. 位数が20の時は Gal=F20, 位数が10の時は Gal=D5, 位数が5 の時は Gal=C5 です. 既約で可解な5次方程式のGalois群はF20,D5,C5の何れかとなります.(参考文献[1][3]) 結果は F20 238個, D5 449個, C5 10個 計697個. 一方,係数が整数で絶対値が10以下,定数項は正で monicな 5次方程式の個数は 21^4*10=1944810個(約200万個) 故に可解な方程式の割合は 697/1944810=0.00035839(約0.036%) 約3000個に1個の割合でしか,可解な5次方程式と出会うことは有りません! 【重要】f(x)=x^5+(a)x^4+(b)x^3+(c)x^2+(d)x+(e)と (-f(-x))=x^5-(a)x^4+(b)x^3-(c)x^2+(d)x-(e) のガロア群は同じなのでeは正の整数のみ挙げています.従って[a,b,c,d,e]が可解ならば,[-a,b,-c,d,-e]も可解です. (イ) 「4次の係数が0」で残りの係数の絶対値が15以下: f(x)=x^5+(a)x^3+(b)x^2+(c)x+(d) (-15≦a,b,c≦15,1≦d≦15, a,b,c,dは整数) のうち既約で可解な方程式を SageMath で数え上げました.これは 主に, アプリを使う方のためです. F20,D5,C5の内訳は次のとおりです. F20 61個, D5 109個, C5 3個 計173個. ################################################################################################# (ア)係数の絶対値が10以下 [[-10, -10, 10, 10, 2], 20] [[-10, 10, 10, -10, 2], 20] [[-6, -1, 10, -6, 1], 5] [[-6, 6, 8, 7, 2], 20] [[-6, 7, 8, -4, 1], 10] [[-6, 8, 6, 2, 2], 20] [[-6, 9, 2, -4, 1], 10] [[-6, 10, -1, -6, 1], 5] [[-6, 10, 5, 6, 4], 10] [[-5, 3, 9, 1, 7], 20] [[-5, 3, 9, 4, 7], 10] [[-5, 5, 5, -5, 2], 20] [[-5, 5, 5, -5, 3], 20] [[-5, 5, 5, -5, 4], 20] [[-5, 5, 5, -5, 5], 20] [[-5, 5, 5, -5, 6], 20] [[-5, 5, 5, -5, 7], 20] [[-5, 5, 5, -5, 8], 20] [[-5, 5, 5, -5, 9], 20] [[-5, 5, 5, -5, 10], 20] [[-5, 5, 5, 0, 3], 10] [[-5, 5, 5, 5, 3], 20] [[-5, 5, 5, 6, 1], 10] [[-5, 7, 0, 1, 1], 10] [[-5, 7, 1, -2, 1], 10] [[-5, 8, 5, 9, 5], 10] [[-5, 9, -5, -4, 5], 10] [[-5, 9, -3, -2, 1], 10] [[-5, 10, -10, 5, 1], 20] [[-5, 10, -10, 5, 2], 20] [[-5, 10, -10, 5, 3], 20] [[-5, 10, -10, 5, 4], 20] [[-5, 10, -10, 5, 5], 20] [[-5, 10, -10, 5, 6], 20] [[-5, 10, -10, 5, 7], 20] [[-5, 10, -10, 5, 8], 20] [[-5, 10, -10, 5, 9], 20] [[-5, 10, -10, 5, 10], 20] [[-5, 10, -5, -9, 9], 10] [[-5, 10, -5, -5, 7], 10] [[-5, 10, 10, 5, 2], 20] [[-4, -9, 0, 4, 1], 10] [[-4, 2, 4, 8, 4], 20] [[-4, 2, 9, -6, 1], 10] [[-4, 3, 1, 3, 7], 20] [[-4, 3, 2, 4, 5], 10] [[-4, 4, 1, -1, 2], 20] [[-4, 4, 1, 4, 1], 10] [[-4, 4, 6, -6, 2], 20] [[-4, 5, 0, 0, 1], 10] [[-4, 6, 1, -9, 10], 20] [[-4, 6, 3, 8, 4], 10] [[-4, 6, 5, -10, 4], 10] [[-4, 7, -2, -2, 1], 10] [[-4, 7, 0, -8, 8], 10] [[-4, 7, 10, -2, 8], 10] [[-4, 8, -8, -2, 8], 20] [[-4, 8, -7, -2, 9], 10] [[-4, 8, -6, 0, 2], 20] [[-4, 8, -5, -6, 9], 10] [[-4, 8, -5, 0, 4], 10] [[-4, 8, 4, -8, 8], 20] [[-4, 8, 7, -6, 1], 10] [[-4, 8, 9, 2, 4], 10] [[-4, 9, -6, -5, 10], 10] [[-4, 9, -5, 3, 1], 10] [[-4, 9, -4, -2, 5], 10] [[-4, 10, 0, -2, 2], 20] [[-3, -7, 1, 4, 1], 10] [[-3, -3, 9, 8, 4], 10] [[-3, -1, 7, 3, 1], 10] [[-3, 0, 0, 6, 6], 20] [[-3, 0, 8, -10, 6], 20] [[-3, 0, 10, 5, 5], 20] [[-3, 1, -1, 8, 7], 10] [[-3, 3, -3, 3, 3], 20] [[-3, 3, -1, 2, 1], 10] [[-3, 3, 3, -1, 1], 10] [[-3, 3, 7, -7, 3], 20] [[-3, 4, -7, 5, 4], 10] [[-3, 4, -1, 3, 1], 10] [[-3, 4, 0, -5, 7], 20] [[-3, 5, -1, -2, 1], 10] [[-3, 5, 1, 0, 4], 10] [[-3, 5, 2, -7, 7], 10] [[-3, 6, -3, 1, 3], 10] [[-3, 6, -2, 4, 4], 20] [[-3, 7, -5, 0, 9], 10] [[-3, 7, -1, -4, 7], 10] [[-3, 7, -1, 3, 9], 10] [[-3, 7, 4, 8, 8], 10] [[-3, 8, -9, 7, 3], 10] [[-3, 8, -8, 8, 8], 20] [[-3, 8, -7, 5, 1], 10] [[-3, 8, -5, -5, 7], 10] [[-3, 8, 0, 1, 6], 20] [[-3, 9, -9, 8, 5], 10] [[-3, 9, -7, 1, 5], 20] [[-3, 10, -10, -3, 9], 20] [[-2, -7, 4, 10, 3], 10] [[-2, -5, 2, 4, 1], 5] [[-2, -5, 9, 5, 3], 10] [[-2, -3, 3, 7, 1], 10] [[-2, -3, 4, 8, 8], 10] [[-2, -3, 6, 9, 2], 10] [[-2, -3, 9, -5, 1], 10] [[-2, -2, 4, 2, 2], 20] [[-2, -2, 7, -4, 1], 10] [[-2, -2, 8, 8, 2], 20] [[-2, -1, -1, 7, 1], 10] [[-2, -1, 4, 3, 2], 10] [[-2, -1, 5, -5, 3], 20] [[-2, -1, 5, -3, 1], 10] [[-2, 0, 3, -2, 1], 10] [[-2, 0, 7, -8, 4], 10] [[-2, 1, -2, 4, 1], 10] [[-2, 1, 1, -1, 1], 10] [[-2, 1, 7, -5, 1], 10] [[-2, 1, 7, 9, 9], 10] [[-2, 2, -7, 5, 6], 20] [[-2, 2, -7, 7, 4], 20] [[-2, 2, -1, 0, 1], 10] [[-2, 2, 3, -3, 4], 20] [[-2, 2, 8, -8, 4], 20] [[-2, 3, -3, 1, 1], 10] [[-2, 3, 0, -2, 1], 10] [[-2, 3, 0, 10, 8], 10] [[-2, 3, 4, -1, 2], 10] [[-2, 3, 6, -10, 8], 10] [[-2, 3, 8, 3, 2], 20] [[-2, 4, -5, 2, 1], 10] [[-2, 4, 3, 10, 4], 10] [[-2, 4, 8, -4, 8], 20] [[-2, 5, -7, 3, 1], 10] [[-2, 5, 2, -6, 9], 10] [[-2, 5, 4, 0, 8], 10] [[-2, 5, 6, -7, 2], 10] [[-2, 5, 8, 4, 1], 10] [[-2, 6, -9, 4, 1], 10] [[-2, 6, -8, -1, 6], 20] [[-2, 6, -8, 7, 6], 20] [[-2, 6, -3, -1, 6], 20] [[-2, 6, 2, 4, 1], 20] [[-2, 6, 8, 7, 6], 20] [[-2, 6, 8, 9, 2], 20] [[-2, 7, -3, 4, 1], 10] [[-2, 7, 0, 4, 1], 10] [[-2, 8, -4, 3, 2], 10] [[-2, 8, -1, 4, 3], 10] [[-2, 9, -5, 2, 3], 10] [[-2, 10, -6, 1, 4], 10] [[-2, 10, 8, -7, 2], 20] [[-1, -5, 3, 8, 3], 10] [[-1, -3, 3, 4, 1], 10] [[-1, -3, 8, 1, 3], 10] [[-1, -3, 9, -4, 2], 10] [[-1, -2, 7, -3, 2], 10] [[-1, -1, -3, 6, 1], 10] [[-1, -1, 3, 2, 1], 10] [[-1, -1, 3, 5, 1], 10] [[-1, -1, 5, -2, 2], 10] [[-1, 0, 1, 3, 1], 20] [[-1, 0, 3, -1, 2], 10] [[-1, 0, 10, -5, 5], 20] [[-1, 1, 1, -2, 1], 10] [[-1, 1, 3, 2, 3], 10] [[-1, 1, 9, -9, 5], 20] [[-1, 2, -5, 1, 3], 10] [[-1, 2, -1, 1, 2], 10] [[-1, 2, 7, -9, 7], 10] [[-1, 3, -3, 2, 2], 10] [[-1, 3, 0, 5, 1], 10] [[-1, 3, 1, -3, 7], 20] [[-1, 3, 2, -1, 3], 10] [[-1, 3, 3, -3, 1], 10] [[-1, 3, 3, 0, 9], 20] [[-1, 3, 3, 4, 7], 10] [[-1, 3, 5, -1, 3], 10] [[-1, 4, -5, 3, 2], 10] [[-1, 4, 4, -4, 4], 20] [[-1, 4, 7, 5, 7], 20] [[-1, 4, 9, 4, 3], 20] [[-1, 5, -7, 4, 2], 10] [[-1, 6, -9, 5, 2], 10] [[-1, 6, 2, -1, 3], 20] [[-1, 7, 2, -5, 5], 10] [[-1, 8, 6, 7, 2], 20] [[0, -10, 5, 10, 1], 5] [[0, -10, 10, 5, 2], 10] [[0, -9, -4, 10, 4], 10] [[0, -9, 9, 4, 3], 10] [[0, -8, -3, 10, 4], 10] [[0, -8, 8, 3, 4], 10] [[0, -7, 7, 2, 5], 10] [[0, -7, 10, -5, 2], 10] [[0, -6, -1, 10, 4], 10] [[0, -6, 6, 1, 6], 10] [[0, -5, 0, 5, 3], 20] [[0, -5, 0, 5, 4], 20] [[0, -5, 0, 5, 5], 20] [[0, -5, 0, 5, 6], 20] [[0, -5, 0, 5, 7], 20] [[0, -5, 0, 5, 8], 20] [[0, -5, 0, 5, 9], 20] [[0, -5, 0, 5, 10], 20] [[0, -5, 0, 10, 4], 10] [[0, -5, 0, 10, 9], 10] [[0, -5, 5, 0, 7], 10] [[0, -5, 7, 8, 5], 10] [[0, -5, 10, -10, 8], 10] [[0, -4, 1, 10, 4], 10] [[0, -4, 4, -1, 8], 10] [[0, -3, -4, 8, 1], 10] [[0, -3, 1, 7, 5], 10] [[0, -3, 2, 6, 3], 10] [[0, -3, 2, 10, 4], 10] [[0, -3, 3, -2, 9], 10] [[0, -2, 2, -3, 10], 10] [[0, -2, 3, 10, 4], 10] [[0, -2, 9, -2, 3], 10] [[0, -1, -10, 8, 9], 10] [[0, -1, -4, 7, 2], 20] [[0, -1, -2, 3, 4], 10] [[0, -1, 2, -2, 1], 10] [[0, -1, 4, 4, 1], 10] [[0, -1, 4, 10, 4], 10] [[0, -1, 7, -1, 3], 10] [[0, 0, -10, 10, 2], 20] [[0, 0, -3, 2, 1], 10] [[0, 0, 0, 0, 2], 20] [[0, 0, 0, 0, 3], 20] [[0, 0, 0, 0, 4], 20] [[0, 0, 0, 0, 5], 20] [[0, 0, 0, 0, 6], 20] [[0, 0, 0, 0, 7], 20] [[0, 0, 0, 0, 8], 20] [[0, 0, 0, 0, 9], 20] [[0, 0, 0, 0, 10], 20] [[0, 0, 5, -5, 8], 20] [[0, 0, 5, -4, 1], 10] [[0, 0, 5, 0, 3], 10] [[0, 0, 5, 10, 4], 10] [[0, 0, 10, -10, 6], 20] [[0, 1, 3, 1, 3], 10] [[0, 1, 6, 4, 3], 10] [[0, 1, 6, 10, 4], 10] [[0, 2, 1, 2, 3], 10] [[0, 2, 4, -1, 4], 20] [[0, 2, 5, -4, 4], 10] [[0, 2, 7, 10, 4], 10] [[0, 2, 8, 9, 8], 10] [[0, 3, -1, 3, 3], 10] [[0, 3, 6, -1, 4], 10] [[0, 3, 8, 6, 9], 10] [[0, 3, 8, 10, 4], 10] [[0, 4, -3, 4, 3], 10] [[0, 4, 4, 8, 8], 20] [[0, 4, 9, 10, 1], 10] [[0, 4, 9, 10, 4], 10] [[0, 5, -5, 5, 3], 10] [[0, 5, 0, 5, 1], 20] [[0, 5, 0, 5, 2], 20] [[0, 5, 0, 5, 3], 20] [[0, 5, 0, 5, 4], 20] [[0, 5, 0, 5, 5], 20] [[0, 5, 0, 5, 6], 20] [[0, 5, 0, 5, 7], 20] [[0, 5, 0, 5, 8], 20] [[0, 5, 0, 5, 9], 20] [[0, 5, 0, 5, 10], 20] [[0, 5, 1, 9, 5], 20] [[0, 5, 10, 0, 5], 10] [[0, 5, 10, 5, 4], 20] [[0, 5, 10, 10, 4], 10] [[0, 6, -7, 6, 3], 10] [[0, 6, 4, -9, 4], 20] [[0, 7, -9, 7, 3], 10] [[0, 7, 3, 5, 5], 10] [[0, 7, 5, 5, 1], 10] [[0, 7, 5, 9, 5], 10] [[0, 7, 10, -6, 5], 10] [[0, 8, 2, 2, 2], 20] [[0, 8, 5, 6, 7], 10] [[0, 9, 5, 3, 9], 10] [[0, 10, 0, 0, 5], 20] [[0, 10, 10, 10, 3], 20] [[1, -10, -9, 3, 1], 10] [[1, -9, -8, 3, 1], 10] [[1, -8, -7, 3, 1], 10] [[1, -8, 8, 8, 8], 20] [[1, -8, 9, -2, 9], 20] [[1, -7, -6, 3, 1], 10] [[1, -6, -5, 3, 1], 10] [[1, -6, 7, -3, 9], 10] [[1, -5, -5, 10, 1], 10] [[1, -5, -4, 3, 1], 10] [[1, -4, -3, 3, 1], 5] [[1, -4, 1, 7, 3], 10] [[1, -4, 4, 2, 2], 20] [[1, -4, 5, -5, 3], 10] [[1, -4, 7, -3, 2], 10] [[1, -3, -2, 3, 1], 10] [[1, -3, 3, -2, 1], 10] [[1, -3, 9, -7, 9], 20] [[1, -2, -7, 3, 7], 10] [[1, -2, -1, 2, 3], 20] [[1, -2, -1, 3, 1], 10] [[1, -2, -1, 7, 7], 10] [[1, -2, 4, 7, 3], 20] [[1, -1, -5, 3, 5], 10] [[1, -1, 0, 3, 1], 10] [[1, -1, 1, 4, 3], 10] [[1, 0, 1, 3, 1], 10] [[1, 0, 5, 0, 5], 20] [[1, 0, 7, -5, 1], 10] [[1, 0, 8, -2, 6], 20] [[1, 0, 9, 1, 4], 10] [[1, 0, 9, 7, 2], 10] [[1, 1, -4, -5, 7], 10] [[1, 1, 2, 3, 1], 10] [[1, 1, 5, 4, 1], 10] [[1, 1, 7, 2, 4], 10] [[1, 2, 2, -5, 3], 20] [[1, 2, 3, -3, 5], 10] [[1, 2, 3, 3, 1], 10] [[1, 2, 4, 1, 1], 20] [[1, 2, 5, -3, 3], 10] [[1, 2, 5, 3, 4], 10] [[1, 3, -3, 2, 7], 10] [[1, 3, 1, 10, 3], 10] [[1, 3, 4, 3, 1], 10] [[1, 3, 7, -1, 5], 10] [[1, 3, 8, 9, 5], 10] [[1, 3, 9, 6, 5], 10] [[1, 4, -4, -1, 2], 20] [[1, 4, -4, 2, 2], 20] [[1, 4, 1, 5, 4], 10] [[1, 4, 2, 1, 1], 20] [[1, 4, 3, 7, 1], 10] [[1, 4, 5, 3, 1], 10] [[1, 5, -1, 6, 4], 10] [[1, 5, 5, 6, 1], 10] [[1, 5, 6, 3, 1], 10] [[1, 6, -3, 7, 4], 10] [[1, 6, 7, 3, 1], 10] [[1, 7, -8, -3, 9], 10] [[1, 7, -5, 8, 4], 10] [[1, 7, 2, 4, 8], 10] [[1, 7, 8, 3, 1], 10] [[1, 7, 10, 5, 1], 10] [[1, 8, -8, 8, 8], 20] [[1, 8, -7, 9, 4], 10] [[1, 8, -1, 7, 1], 20] [[1, 8, 9, 3, 1], 10] [[1, 9, -9, 10, 4], 10] [[1, 9, 7, 8, 3], 10] [[1, 9, 10, 3, 1], 10] [[1, 10, -10, 5, 5], 20] [[2, -9, 5, 4, 5], 10] [[2, -7, 1, -3, 9], 10] [[2, -7, 7, -7, 5], 10] [[2, -6, 5, -4, 9], 10] [[2, -5, 4, -2, 1], 10] [[2, -4, 0, 8, 4], 20] [[2, -4, 8, -6, 4], 20] [[2, -4, 8, 2, 4], 20] [[2, -3, -7, 5, 3], 10] [[2, -3, -4, 7, 8], 10] [[2, -3, 0, 0, 1], 10] [[2, -2, -8, -1, 10], 20] [[2, -2, 0, -1, 2], 20] [[2, -2, 5, 6, 9], 10] [[2, -1, -8, 3, 6], 10] [[2, -1, 2, -2, 3], 10] [[2, -1, 3, -3, 1], 10] [[2, 0, -10, 0, 10], 20] [[2, 0, 10, 0, 10], 20] [[2, 1, -3, 10, 5], 10] [[2, 1, -2, -1, 4], 20] [[2, 1, 0, 2, 3], 10] [[2, 1, 4, -2, 5], 10] [[2, 1, 4, 7, 4], 10] [[2, 1, 8, 9, 4], 20] [[2, 2, -4, 9, 10], 10] [[2, 2, -3, -4, 4], 10] [[2, 2, -2, 9, 4], 10] [[2, 2, 3, 6, 5], 10] [[2, 2, 4, 0, 4], 20] [[2, 2, 7, -6, 4], 10] [[2, 2, 10, -10, 3], 20] [[2, 3, -1, -1, 1], 10] [[2, 3, -1, 8, 3], 10] [[2, 3, 6, 0, 7], 10] [[2, 3, 6, 4, 1], 10] [[2, 3, 8, -1, 6], 10] [[2, 3, 8, 10, 8], 10] [[2, 3, 9, 1, 7], 10] [[2, 3, 9, 5, 5], 10] [[2, 4, -8, 2, 4], 20] [[2, 4, 0, 7, 2], 10] [[2, 4, 7, 6, 5], 10] [[2, 5, -6, -6, 5], 10] [[2, 5, 1, 6, 1], 10] [[2, 5, 5, 7, 5], 10] [[2, 5, 8, 4, 9], 10] [[2, 6, 3, 8, 5], 10] [[2, 6, 7, 6, 7], 10] [[2, 6, 8, -9, 10], 20] [[2, 6, 9, 8, 5], 10] [[2, 7, 1, 9, 5], 10] [[2, 8, -8, -2, 3], 20] [[2, 8, -1, 10, 5], 10] [[2, 8, 2, -8, 5], 20] [[2, 9, 0, -5, 4], 20] [[2, 9, 10, 6, 1], 10] [[2, 10, -3, -4, 3], 10] [[2, 10, 10, -10, 10], 20] [[3, -9, -10, 1, 1], 10] [[3, -8, -9, 1, 1], 10] [[3, -8, -3, 1, 10], 10] [[3, -8, 4, 3, 9], 20] [[3, -7, -8, 1, 1], 10] [[3, -7, 5, -2, 1], 10] [[3, -6, -7, 1, 1], 10] [[3, -5, -6, 1, 1], 10] [[3, -5, 3, -2, 3], 10] [[3, -5, 9, -4, 1], 10] [[3, -4, -5, 1, 1], 10] [[3, -4, 1, 3, 5], 10] [[3, -3, -4, 1, 1], 5] [[3, -3, 4, -1, 5], 10] [[3, -3, 7, -6, 9], 10] [[3, -2, -3, 1, 1], 10] [[3, -1, -8, 1, 7], 10] [[3, -1, -4, 7, 5], 10] [[3, -1, -2, 1, 1], 10] [[3, -1, 4, -3, 1], 10] [[3, -1, 7, -1, 2], 20] [[3, -1, 10, -5, 7], 10] [[3, -1, 10, 4, 8], 10] [[3, 0, -4, 1, 5], 20] [[3, 0, -1, 1, 1], 10] [[3, 1, -6, -1, 5], 10] [[3, 1, -1, 5, 7], 10] [[3, 1, 0, -1, 1], 20] [[3, 1, 0, 1, 1], 10] [[3, 1, 3, -10, 5], 10] [[3, 2, 1, 1, 1], 10] [[3, 2, 5, -2, 5], 20] [[3, 2, 5, 3, 2], 10] [[3, 3, -1, 0, 3], 10] [[3, 3, 2, 1, 1], 10] [[3, 3, 6, -5, 3], 10] [[3, 3, 8, 9, 3], 10] [[3, 3, 9, -1, 7], 10] [[3, 4, -3, -6, 5], 20] [[3, 4, -3, -4, 5], 20] [[3, 4, 3, 1, 1], 10] [[3, 4, 7, 6, 5], 20] [[3, 5, 4, 1, 1], 10] [[3, 5, 7, 4, 1], 10] [[3, 5, 8, 7, 1], 10] [[3, 6, 5, 1, 1], 10] [[3, 7, -1, -3, 1], 10] [[3, 7, 6, 1, 1], 10] [[3, 7, 8, 9, 1], 10] [[3, 8, 7, 1, 1], 10] [[3, 8, 8, -2, 2], 20] [[3, 8, 8, 6, 10], 20] [[3, 9, 3, 4, 3], 10] [[3, 9, 8, 1, 1], 10] [[3, 10, 9, 1, 1], 10] [[4, -10, -9, 6, 4], 10] [[4, -9, -8, 6, 4], 10] [[4, -9, -5, 9, 1], 5] [[4, -9, 6, -2, 1], 10] [[4, -7, -6, 6, 4], 10] [[4, -7, 6, -4, 5], 10] [[4, -6, -5, 6, 4], 10] [[4, -6, 4, -1, 8], 20] [[4, -6, 4, 9, 8], 20] [[4, -5, -4, 6, 4], 10] [[4, -4, -3, 6, 4], 10] [[4, -4, 2, 6, 2], 20] [[4, -3, -8, 6, 9], 10] [[4, -3, -2, -2, 3], 20] [[4, -3, -2, 6, 4], 10] [[4, -3, 7, -2, 1], 10] [[4, -2, -4, 2, 2], 20] [[4, -2, -1, 6, 4], 10] [[4, -2, 1, -2, 1], 10] [[4, -1, -4, -2, 3], 10] [[4, -1, 0, 6, 4], 10] [[4, -1, 10, -3, 5], 20] [[4, -1, 10, 7, 4], 10] [[4, 0, -9, -4, 1], 10] [[4, 0, -8, 8, 8], 20] [[4, 0, 1, 6, 4], 10] [[4, 0, 7, -2, 1], 10] [[4, 0, 10, 0, 5], 20] [[4, 1, -8, 0, 9], 10] [[4, 1, -7, -3, 1], 10] [[4, 1, -6, 6, 9], 10] [[4, 1, 2, 6, 4], 10] [[4, 1, 4, -4, 1], 10] [[4, 2, -5, -2, 1], 5] [[4, 2, 3, -6, 7], 10] [[4, 2, 3, 6, 4], 10] [[4, 2, 6, -2, 1], 20] [[4, 2, 8, 9, 4], 10] [[4, 3, -3, -1, 1], 10] [[4, 3, -2, 2, 5], 10] [[4, 3, 3, 9, 9], 10] [[4, 3, 4, 6, 4], 10] [[4, 3, 9, 1, 5], 10] [[4, 3, 10, -1, 8], 10] [[4, 4, -9, -2, 4], 10] [[4, 4, -1, 0, 1], 10] [[4, 4, 5, 6, 4], 10] [[4, 4, 7, -8, 4], 10] [[4, 5, -8, 6, 5], 10] [[4, 5, -6, 6, 1], 10] [[4, 5, -2, -2, 3], 10] [[4, 5, 1, 1, 1], 10] [[4, 5, 4, 6, 5], 10] [[4, 5, 4, 9, 8], 10] [[4, 5, 6, 6, 4], 10] [[4, 5, 10, 5, 5], 20] [[4, 6, -5, -4, 3], 10] [[4, 6, 3, 2, 1], 10] [[4, 6, 5, 6, 5], 20] [[4, 6, 7, 6, 4], 10] [[4, 7, -4, -7, 6], 20] [[4, 7, 5, 3, 1], 10] [[4, 7, 8, 4, 1], 10] [[4, 8, 5, -2, 1], 10] [[4, 8, 7, 4, 1], 10] [[4, 8, 9, 6, 4], 10] [[4, 9, -6, -1, 2], 10] [[4, 9, 9, 5, 1], 10] [[4, 9, 10, 6, 4], 10] [[4, 10, 5, -7, 2], 20] [[5, -10, 10, -5, 1], 20] [[5, -10, 10, 5, 4], 20] [[5, -9, 9, -6, 7], 10] [[5, -8, 5, 1, 5], 10] [[5, -7, 8, -3, 1], 10] [[5, -5, 5, -5, 3], 20] [[5, -2, 6, 1, 5], 20] [[5, -2, 7, -7, 9], 20] [[5, 0, -10, 0, 8], 10] [[5, 0, -3, -9, 7], 10] [[5, 0, 0, -10, 6], 20] [[5, 0, 0, 5, 3], 20] [[5, 0, 3, -1, 1], 10] [[5, 0, 5, 0, 1], 20] [[5, 0, 10, -5, 2], 20] [[5, 0, 10, 0, 4], 20] [[5, 1, -8, 0, 8], 10] [[5, 1, -5, -4, 10], 20] [[5, 2, -6, 0, 8], 10] [[5, 3, -4, 0, 8], 10] [[5, 3, -1, -1, 1], 10] [[5, 3, 8, -8, 8], 10] [[5, 4, -9, -5, 8], 10] [[5, 4, -7, -1, 2], 10] [[5, 4, -2, 0, 8], 10] [[5, 4, 4, 2, 10], 20] [[5, 5, -5, -5, 4], 20] [[5, 5, -5, -5, 5], 20] [[5, 5, -5, -5, 6], 20] [[5, 5, -5, -5, 7], 20] [[5, 5, -5, -5, 8], 20] [[5, 5, -5, -5, 9], 20] [[5, 5, -5, -5, 10], 20] [[5, 5, -5, 0, 2], 10] [[5, 5, -5, 0, 10], 10] [[5, 5, 0, 0, 8], 10] [[5, 5, 5, 0, 4], 10] [[5, 5, 7, 0, 1], 10] [[5, 5, 9, -4, 4], 20] [[5, 6, -3, 1, 2], 10] [[5, 6, 2, 0, 8], 10] [[5, 6, 5, -7, 3], 10] [[5, 7, -3, -4, 3], 10] [[5, 7, -1, 2, 2], 10] [[5, 7, 3, 6, 9], 10] [[5, 7, 4, 0, 8], 10] [[5, 8, 1, 3, 2], 10] [[5, 8, 6, 0, 8], 10] [[5, 9, -10, 1, 5], 10] [[5, 9, -3, -10, 7], 10] [[5, 9, 3, 1, 5], 20] [[5, 9, 3, 4, 2], 10] [[5, 9, 5, 1, 5], 10] [[5, 9, 8, 0, 8], 10] [[5, 9, 9, 4, 1], 10] [[5, 9, 9, 9, 1], 10] [[5, 10, -5, -10, 7], 20] [[5, 10, 0, -5, 3], 20] [[5, 10, 0, 5, 5], 20] [[5, 10, 1, 1, 2], 10] [[5, 10, 5, 5, 2], 10] [[5, 10, 7, 1, 1], 10] [[5, 10, 10, 0, 8], 10] [[5, 10, 10, 5, 3], 20] [[5, 10, 10, 5, 4], 20] [[5, 10, 10, 5, 5], 20] [[5, 10, 10, 5, 6], 20] [[5, 10, 10, 5, 7], 20] [[5, 10, 10, 5, 8], 20] [[5, 10, 10, 5, 9], 20] [[5, 10, 10, 5, 10], 20] [[6, -6, 5, 4, 1], 10] [[6, -6, 6, -4, 2], 20] [[6, -4, 8, -4, 8], 20] [[6, -3, -1, -1, 1], 10] [[6, -1, -4, -1, 2], 20] [[6, 0, -8, -2, 4], 20] [[6, 0, 5, -5, 10], 20] [[6, 1, 5, 2, 1], 10] [[6, 2, 4, 8, 4], 20] [[6, 3, 0, -1, 2], 10] [[6, 4, 6, -6, 7], 20] [[6, 5, 5, -5, 1], 10] [[6, 5, 5, 1, 1], 10] [[6, 5, 8, 0, 8], 10] [[6, 6, -8, 9, 10], 20] [[6, 6, 1, 1, 10], 20] [[6, 7, -9, 1, 3], 10] [[6, 7, -6, 3, 4], 20] [[6, 8, -8, -8, 8], 20] [[6, 8, -7, 2, 3], 10] [[6, 8, -1, 8, 1], 10] [[6, 8, 5, -10, 4], 10] [[6, 8, 5, 2, 9], 10] [[6, 9, -9, -7, 5], 10] [[6, 9, -5, 3, 3], 10] [[6, 9, -4, -6, 3], 10] [[6, 10, -3, 4, 3], 10] [[6, 10, 5, 6, 9], 10] [[6, 10, 8, 7, 6], 20] [[6, 10, 9, 2, 1], 10] [[7, -9, 8, 0, 8], 20] [[7, -5, -5, 5, 5], 20] [[7, -4, 8, 4, 4], 20] [[7, -3, 9, 5, 3], 20] [[7, -2, -3, -2, 3], 20] [[7, -1, -1, -2, 1], 10] [[7, -1, 8, 1, 1], 20] [[7, 0, -10, 1, 2], 20] [[7, 2, 2, 5, 2], 20] [[7, 3, -3, -2, 1], 10] [[7, 3, 1, -1, 3], 10] [[7, 3, 4, 1, 1], 10] [[7, 4, 0, 4, 4], 10] [[7, 5, 8, 3, 3], 10] [[7, 8, 5, 3, 1], 10] [[7, 9, 0, 0, 8], 10] [[7, 9, 7, 9, 7], 10] [[7, 10, -10, -5, 5], 20] [[8, -6, 3, -1, 2], 20] [[8, -6, 8, 2, 6], 20] [[8, -4, -3, 0, 1], 10] [[8, -3, -2, -3, 4], 20] [[8, -1, 8, 6, 1], 10] [[8, 2, 4, 1, 4], 20] [[8, 3, 2, -1, 4], 10] [[8, 6, -3, -6, 4], 10] [[8, 7, 3, 1, 5], 10] [[8, 8, -2, -2, 2], 20] [[9, -5, -9, 4, 1], 5] [[9, -4, -9, -5, 9], 10] [[9, -4, -1, -4, 5], 20] [[9, -2, -3, 7, 4], 10] [[9, -2, 6, -3, 2], 20] [[9, 3, 3, -1, 5], 10] [[9, 8, 7, 3, 1], 10] [[9, 9, -1, -1, 3], 20] [[9, 9, 9, 5, 1], 10] [[10, -10, 5, -5, 4], 20] [[10, -8, 8, -5, 2], 10] [[10, -5, -10, 5, 5], 20] [[10, -5, -5, 1, 1], 10] [[10, -5, 0, -5, 6], 20] [[10, -5, 10, -5, 3], 20] [[10, -2, 8, -1, 2], 20] [[10, 0, -10, 0, 2], 20] [[10, 0, 10, 0, 2], 20] [[10, 3, 4, -1, 6], 10] [[10, 5, -10, 0, 1], 5] [[10, 5, -4, 3, 4], 20] [[10, 5, 0, -10, 8], 10] [[10, 9, 4, 0, 1], 10] [[10, 10, 0, 0, 4], 20] [[10, 10, 5, 4, 4], 10] [[10, 10, 5, 5, 10], 20] ########################################################################## (イ)「4次の係数が0」かつ「残りの係数の絶対値が15以下」 [[-15, -10, 10, 4], 10] [[-15, -10, 10, 7], 5] [[-14, -14, 9, 2], 10] [[-14, -9, 10, 4], 10] [[-13, -13, 8, 1], 10] [[-13, -8, 10, 4], 10] [[-12, -7, 10, 4], 10] [[-11, -11, 11, 11], 5] [[-11, -10, 11, 10],10] [[-11, -6, 10, 4], 10] [[-11, 11, 6, 1], 10] [[-10, 5, 10, 1], 5] [[-10, 10, 5, 2], 10] [[-9, -4, 10, 4], 10] [[-9, 9, 4, 3], 10] [[-9, 12, -6, 12], 20] [[-8, -3, 10, 4], 10] [[-8, 8, 3, 4], 10] [[-7, 7, 2, 5], 10] [[-7, 10, -5, 2],10] [[-6, -1, 10, 4], 10] [[-6, 6, 1, 6], 10] [[-6, 12, -9, 12], 20] [[-5, 0, 5, 3], 20] [[-5, 0, 5, 4], 20] [[-5, 0, 5, 5], 20] [[-5, 0, 5, 6], 20] [[-5, 0, 5, 7], 20] [[-5, 0, 5, 8], 20] [[-5, 0, 5, 9], 20] [[-5, 0, 5, 10], 20] [[-5, 0, 5, 11], 20] [[-5, 0, 5, 12], 20] [[-5, 0, 5, 13], 20] [[-5, 0, 5, 14], 20] [[-5, 0, 5, 15], 20] [[-5, 0, 10, 4], 10] [[-5, 0, 10, 9], 10] [[-5, 0, 15, 14], 20] [[-5, 5, 0, 7], 10] [[-5, 7, 8, 5], 10] [[-5, 10, -10, 8], 10] [[-5, 11, -3, 9], 10] [[-5, 12, -14, 7], 10] [[-5, 15, -5, 3], 10] [[-4, 1, 10, 4], 10] [[-4, 4, -1, 8], 10] [[-4, 7, -14, 13], 10] [[-4, 13, -4, 3], 10] [[-3, -4, 8, 1], 10] [[-3, 1, 7, 5], 10] [[-3, 2, 6, 3], 10] [[-3, 2, 10, 4], 10] [[-3, 3, -2, 9], 10] [[-3, 10, -13, 14], 10] [[-3, 11, -3, 3], 10] [[-2, 2, -3, 10], 10] [[-2, 3, 10, 4], 10] [[-2, 7, -12, 7], 10] [[-2, 9, -2, 3], 10] [[-1, -10, 8, 9], 10] [[-1, -7, 1, 11], 10] [[-1, -4, 7, 2], 20] [[-1, -2, 3, 4], 10] [[-1, 1, -4, 11],10] [[-1, 2, -2, 1], 10] [[-1, 4, 4, 1], 10] [[-1, 4, 10, 4],10] [[-1, 7, -1, 3], 10] [[-1, 11, -13, 13], 10] [[0, -15, 15, 6], 20] [[0, -10, 10, 2], 20] [[0, -5, 0, 15], 10] [[0, -3, 2, 1], 10] [[0, 0, -5, 12], 10] [[0, 0, 0, 2], 20] [[0, 0, 0, 3], 20] [[0, 0, 0, 4], 20] [[0, 0, 0, 5], 20] [[0, 0, 0, 6], 20] [[0, 0, 0, 7], 20] [[0, 0, 0, 8], 20] [[0, 0, 0, 9], 20] [[0, 0, 0, 10], 20] [[0, 0, 0, 11], 20] [[0, 0, 0, 12], 20] [[0, 0, 0, 13], 20] [[0, 0, 0, 14], 20] [[0, 0, 0, 15], 20] [[0, 0, 15, 12], 20] [[0, 5, -5, 8], 20] [[0, 5, -4, 1], 10] [[0, 5, 0, 3], 10] [[0, 5, 10, 4], 10] [[0, 9, 14, 4], 10] [[0, 10, -10, 6], 20] [[0, 15, -15, 12], 20] [[0, 15, 15, 14], 20] [[1, -1, -6, 13], 10] [[1, 2, 12, 9], 10] [[1, 3, 1, 3], 10] [[1, 6, 4, 3], 10] [[1, 6, 10, 4], 10] [[1, 8, -10, 13], 10] [[1, 10, -12, 8], 10] [[2, -2, -7, 14], 10] [[2, 1, 2, 3], 10] [[2, 4, -1, 4], 20] [[2, 5, -4, 4], 10] [[2, 7, 10, 4], 10] [[2, 8, 9, 8], 10] [[3, -3, -8, 15] 10] [[3, -1, 3, 3], 10] [[3, 3, -13, 13], 10] [[3, 6, -1, 4], 10] [[3, 8, 6, 9], 10] [[3, 8, 10, 4], 10] [[4, -9, 14, 4], 20] [[4, -3, 4, 3], 10] [[4, 4, 8, 8], 20] [[4, 5, 12, 4],10] [[4, 9, 10, 1], 10] [[4, 9, 10, 4], 10] [[5, -5, 5, 3], 10] [[5, 0, 5, 1], 20] [[5, 0, 5, 2], 20] [[5, 0, 5, 3], 20] [[5, 0, 5, 4], 20] [[5, 0, 5, 5], 20] [[5, 0, 5, 6], 20] [[5, 0, 5, 7], 20] [[5, 0, 5, 8], 20] [[5, 0, 5, 9], 20] [[5, 0, 5, 10], 20] [[5, 0, 5, 12], 20] [[5, 0, 5, 13], 20] [[5, 0, 5, 14], 20] [[5, 0, 5, 15], 20] [[5, 1, 9, 5], 20] [[5, 5, 15, 1], 10] [[5, 10, 0, 5], 10] [[5, 10, 5, 4], 20] [[5, 10, 10, 4], 10] [[6, -7, 6, 3], 10] [[6, 4, -9, 4], 20] [[6, 5, 12, 3], 10] [[6, 11, 10, 4], 10] [[7, -9, 7, 3], 10] [[7, 3, 5, 5], 10] [[7, 5, 5, 1], 10] [[7, 5, 9, 5], 10] [[7, 10, -6, 5], 10] [[7, 12, 10, 4], 10] [[8, -11, 8, 3], 10] [[8, 2, 2, 2], 20] [[8, 5, 6, 7], 10] [[8, 13, 10, 4],10] [[9, -13, 9, 3], 10] [[9, 5, 3, 9], 10] [[9, 14, 10, 4], 10] [[10, -15, 10, 3], 10] [[10, 0, 0, 5], 20] [[10, 5, 0, 11],10] [[10, 10, 10, 3], 20] [[10, 12, -11, 4],10] [[10, 15, 10, 4], 10] [[10, 15, 10, 12], 10] [[11, -2, 0, 7], 10] [[11, -2, 4, 8], 10] [[11, 5, -3, 13], 10] [[12, 5, -6, 15], 10] [[13, -8, 12, 7], 10] [[13, 3, 1, 1], 10]]