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if 4^n + 2^n + 1 is a prime then n = 3^k

Source: Indian Postal Coaching 2007 set 3 p3

May 25, 2020
power of 3number theoryprime

Problem Statement

Suppose nn is a natural number such that 4n+2n+14^n + 2^n + 1 is a prime. Prove that n=3kn = 3^k for some nonnegative integer kk.
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