Some conjectures on congruences

Abstract

Let $p$ be an odd prime. In the paper we collect the author's various conjectures on congruences modulo $p$ or $p^2$, which are concerned with sums of binomial coefficients, Lucas sequences, power residues and special binary quadratic forms.

Conjecture 4.46 is new

References in corpus (4)

• On Apery numbers and generalized central trinomial coefficients
• Some supercongruences modulo $p^2$
• Jacobsthal sums, Legendre polynomials and binary quadratic forms
• Quartic, octic residues and binary quadratic forms

Cited by in corpus (3)

• Proof of two supercongruences conjectured by Z.-W.Sun involving Catalan-Larcombe-French numbers
• A rapidly converging Ramanujan-type series for Catalan's constant
• Congruences involving Franel and Catalan-Larcombe-French numbers