24th ASU 1990 Problem 21 For which positive integers n is 3 2n+1 - 2 2n+1 - 6 n composite?
all n ≠ 1 Solution 3 2n+1 - 2 2n+1 - 6 n = (3 n - 2 n )(3 n+1 + 2 n+1 ), so it is certainly composite for n > 1. For n = 1, it is 27-8-6 = 13, which is prime. Thanks to Suat Namli 24th ASU 1990 © John Scholes jscholes@kalva.demon.co.uk 3 March 2004 Last corrected/updated 3 Mar 04