Hint to puzzle 144: Difference of two nth powers
Let p be a prime factor of n and k be the largest positive integer such that pk divides n. We aim to show that pk divides (an − bn)/(a − b). Begin by assuming that p divides a − b.
Let p be a prime factor of n and k be the largest positive integer such that pk divides n. We aim to show that pk divides (an − bn)/(a − b). Begin by assuming that p divides a − b.