Congruences for Fourth Powers of Generalized Central Trinomial Coefficients
Published:Dec 30, 2025 11:24
•1 min read
•ArXiv
Analysis
This paper investigates congruences modulo p^3 and p^4 for sums involving the fourth powers of generalized central trinomial coefficients. The results contribute to the understanding of number-theoretic properties of these coefficients, particularly for the special case of central trinomial coefficients. The paper's focus on higher-order congruences (modulo p^3 and p^4) suggests a deeper exploration of the arithmetic behavior compared to simpler modular analyses. The specific result for b=c=1 provides a concrete example and connects the findings to the Fermat quotient, highlighting the paper's relevance to number theory.
Key Takeaways
- •The paper focuses on congruences involving the fourth powers of generalized central trinomial coefficients.
- •It establishes congruences modulo p^3 and p^4.
- •A specific result is provided for the case b=c=1, connecting the findings to the Fermat quotient.
Reference
“The paper establishes congruences modulo p^3 and p^4 for sums of the form ∑(2k+1)^(2a+1)ε^k T_k(b,c)^4 / d^(2k).”