Question

已知3的n次方+11的m次方可被10整除,求证3的n+4次方+11的m+2次方也能被10整除

Answer 1

设3^n+11^m=10K(K为正整数),

则3^n=10K-11^m

3^(n+4)+11^(m+2)

=81(10K-11^m)+121*11^m

=510K+(121-81)*11^m

=510K+40*11^m

=10[51K+4*11^m]

k、m都是正整数,

∴3^(n+4)+11^(m+2)被10整除.