■iのn乗(その31)
[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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