Hello guys could anyone help find a solution to this problem,

Show that:

3 x 5^(2n-1) + 2^(3n-2) is divisble by 17 (for every n on N*)

This is what i did :

verification for n = 1.

then we assume it is divisible for n and show it is also divisble for n+1

3 x 5^(2n+2-1) + 2^(3n+3-2)

= 3 x 5^(2n+1) + 2^(3n+1)

= 3 x 5^(2n-1) x 5^2 + 2^(3n-2) x 2^3

i tried a lot of things but i couldnt find the solutions.