When is \(a^{n}+1\) the sum of two squares?

DOI10.2140/involve.2019.12.585zbMath1428.11072arXiv1609.04391OpenAlexW2519834410MaRDI QIDQ2424258

Jeremy Rouse, Pan Yue, Kylie Hess, Saimon Islam, Aaron Schmitt, Emily Stamm, Terrin Warren, Greg Dresden

Publication date: 24 June 2019

Published in: Involve (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.04391

zbMATH Keywords

cyclotomic polynomialsFermat's two squares theorem

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Polynomials in number theory (11C08)

Cites Work

• On the gaps between numbers which are sums of two squares
• Bounded gaps between primes
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• Some properties of the cyclotomic polynomial
• On the intervals between numbers that are sums of two squares
• On Divisors of Fermat, Fibonacci, Lucas, and Lehmer Numbers
• Long gaps between primes
• Primes of the type φ(x, y)+A where φ is a quadratic form
• Small gaps between primes

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