The paper gives exact p-adic valuations or lower bounds for s(ap, ap-k) and derives a recursive pattern that partially proves Lengyel's conjecture for odd k.
Adelberg, The p-adic analysis of Stirling numbers via higher order Bernoul li numbers, Int
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On the $p$-adic properties of Stirling numbers of the first kind
The paper gives exact p-adic valuations or lower bounds for s(ap, ap-k) and derives a recursive pattern that partially proves Lengyel's conjecture for odd k.