On the p-adic valuations of values of Legendre polynomials

Puntos clave

• An explicit formula for p-adic valuation of Legendre polynomials is derived, enhancing previous theories.
• The study provides a new approach to an existing conjecture related to these polynomials and primes.
• This research also addresses a problem posed by Cigler, contributing to the field of number theory.
• Results are significant for understanding properties of Legendre polynomials in the context of p-adic analysis.