■1000!/10^250は整数であるか? (その40)

[Q]a^nの下1桁と元の数aの下1桁が同じになるnを求めよ.

[A]

a の下1桁:0,1,2,3,4,5,6,7,8,9

a^2の下1桁:0,1,4,9,6,5,6,9,4,1

a^3の下1桁:0,1,8,7,4,5,6,3,2,9

a^4の下1桁:0,1,6,1,6,5,6,1,6,1

a^5の下1桁:0,1,2,3,4,5,6,7,8,9

a^6の下1桁:0,1,4,9,6,5,6,9,4,1

a^7の下1桁:0,1,8,7,4,5,6,3,2,9

a^8の下1桁:0,1,6,1,6,5,6,1,6,1

a^5の下1桁:0,1,2,3,4,5,6,7,8,9

5乗,9乗,13乗,・・・と4乗ずつ増えていく.

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