The positive integers a, b, c are such that there are triangles with sides an, bn, cn for all positive integers n. Show that at least two of a, b, c must be equal.
Solution
Suppose not. There is no loss of generality in taking a < b < c and b = 1. But now for n sufficiently large cn > 2. Then cn > 2 > an + bn. Contradiction.
© John Scholes
jscholes@kalva.demon.co.uk
1 Nov 2003
Last corrected/updated 1 Nov 03