Question

Prove that for a positive integer n we have that 3^3n+3 26n - 27 is divisible by 169.​

Answer 1

Answer:

From here, it's quite obvious now, since 13 divides both multipliers. and the red part is divided by 169=132 by the inductive assumption, and the second summand is clearly divided by 132 so we have finished. Use congruences. 3 has order 3 modulo 13, hence 33n+3−26n−27≡1n+1−0−1=0.