The paper proves the Aliniaeifard-Li conjecture, derives identity (1.3) and a q-analog (2.2), and uses them to give new proofs of the Genocchi divisibility theorem and Foata's q-tangent divisibility.
Foata, Further divisibility properties of theq-tangent numbers, Proc
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An identity relating Catalan numbers to tangent numbers with arithmetic applications
The paper proves the Aliniaeifard-Li conjecture, derives identity (1.3) and a q-analog (2.2), and uses them to give new proofs of the Genocchi divisibility theorem and Foata's q-tangent divisibility.