Which is larger, where n is a natural number:

99^{n} + 100^{n} or 101^{n} ?

(In reply to

re: Near Analytic Solution - the proof you asked for by pcbouhid)

Thanks, PCB, for a splendid analytical proof of A(48) < 1. This indeed completes the solution of the given problem.

I came across this problem in the olympiad section of a local journal in 1993 (without solution).

I have been trying ever since for a comprehensive analytical proof that A(48) <1 for the last 15 years, but my endeavors in that direction failed to reach their fruition, till I visualised your proof just now.