Question

145⁸⁹+3²º²º除以13的余数是多少？

不是2002

Answer 1

145的89次方+3的2020次方
=(143+2)的89次方+3×3的2019次方
=(13×11+2)的89次方+3×(3³)的673次方
=13k+2的89次方+3×(13×2+1)的673次方
=13k+2×2的88次方+3×(13×2+1)的673次方
=13k+2×(2的4次方)的22次方+3×(13×2+1)的673次方
=13k+2×(13+3)的22次方+3×(13×2+1)的673次方
=13k+13m+2×3的22次方+13n+3×1的673次方
=13k+13m+2×3×3的21次方+13n+3
=13k+13m+6×(3³)的7次方+13n+3

=13k+13m+6×(13×2+1)的7次方+13n+3

=13k+13m+13s+6×1的7次方+13n+3
=13k+13m+13s+13n+9

除以13时，余数是9