Question
Given 3^n+m is divisible by 13. Prove 3^{n+3}+m is also divisible by 13.
Answer
3^n+m=13k
3^{n+3}+m
=27\cdotp 3^n+13k-3^n
=26\cdotp 3^n+13k
Given 3^n+m is divisible by 13. Prove 3^{n+3}+m is also divisible by 13.
3^n+m=13k
3^{n+3}+m
=27\cdotp 3^n+13k-3^n
=26\cdotp 3^n+13k