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

Reese Scott

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

Reese Scott

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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.

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Reese Scott. 2006-08-31. Elementary treatment of $p^a \pm p^b + 1 = x^2$. https://arxiv.org/abs/math/0608796

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