maths Maths Puzzle

Let a, b, n, and m be positive integers, with n > 1. Show that an + bn = 2m implies a = b.

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maths Other Question

The smallest distance between any two of six towns is m miles. The largest distance between any two of the towns is M miles. Show that M/m greater than or equal to root 3. Assume the land is flat. Let a, b, and n be positive integers, with a not equal to b. Show that n divides an − bn implies n divides (an − bn)/(a − b).