On Some Congruence Conjectures Involving Binary Quadratic Forms
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Open Access
- 22 October 2025
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Publications of the Research Institute for Mathematical Sciences
- Vol. 61 (4) , 611-625
Abstract
In this paper, we mainly prove some congruence conjectures of Z.-H. Sun, for example, let p be a prime such that p\equiv1\pmod6 and p=x^{2}+3y^{2} . Then p\sum_{k=0}^{p-1}\frac{\binom{2k}k^{2}}{(3k+1)16^{k}}\equiv 4x^{2} -2p -{\frac{p^{2}}{4x^{2}}}\pmod{p^3} .Keywords
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