Question

Prove by induction that this is divisible by 228 for any n (natural number).

Answer 1

\[1561^n+712^n-1225^n-364^n\]

Answer 2

For proof by induction:
1. Show this is true for n=1 (simple)
2. Assume it is true for some n=k
3. Then show that this implies it is also true for n=k+1

The last step is the trickiest as you will get to a step where you will need to use induction again to prove that some intermediate expression is always a multiple of 19.

Expressing each constant as a product of its prime factors will help here.