Elementary treatment of $p^a\pm p^b+1=x^2$

Abstract

We give a shorter simpler proof of a result of Szalay on the equation $2^a+2^b+1=z^2$. 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.

Cited by in corpus (1)

• ABC Conjecture: $ABC=2^m{p}^n{q}^r$ with Fermat or Mersenne Primes