Elementary treatment of p^a ± p^b + 1 = x²

2006/08/31 by Scott, Reese
#11D61 #11D99 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0608796

Abstract

We give a shorter simpler proof of a result of Szalay on the equation 2^a + 2^b + 1 = z². We give an elementary proof of a result of Luca on the equation of the title for prime p > 2. The elementary treatment is made possible by a lemma which is also useful for other Diophantine equations.

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