Question

设3的n次方+m能被10整除,试证明3的3n+4次方+m也能被10整除.

Answer 1

证明:
3^n+m能被10整除
设商为k,显然k为整数,
则3^n+m=10k
3^n=10k-m,
从而
3^(n+4)+m
=3^n*3^4+m
=(10k-m)*81+m
=81*10k-81m+m
=81*10k-80m
=(81k-8m)*10
所以
3^(n+4)+m也能被10整除.