This paper finds explicit formulas for p-adic valuation of Legendre polynomials at a prime, generalizing a conjecture and addressing Cigler's problem.
We prove an explicit formula for the p-adic valuation of the Legendre polynomials Pₙ(x) evaluated at a prime p, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017.
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Alekseyev et al. (2025) studied this question.
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