2 papers
math.NT2020
Report on Zhi-Wei Sun's "1-3-5 conjecture" and some of its refinements
António Machiavelo, Rogério Reis, Nikolaos Tsopanidis
We report here on the computational verification of a refinement of Zhi-Wei Sun's "1-3-5 conjecture" for all natural numbers up to 105 103 560 126. This, together with a result of…
math.NT2020
Zhi-Wei Sun's 1-3-5 Conjecture and Variations
António Machiavelo, Nikolaos Tsopanidis
In this paper, using quaternion arithmetic in the ring of Lipschitz integers, we present a proof of Zhì-Wěi Sūn's "1-3-5 conjecture" for integral solutions, and for all natural num…