Open Research Index

Erdős Problem 935: powerful parts of products of consecutive integers

Daniel Veljjanoski

Palomar Registrypalomar/PALOMAR-2026-11-01-000027Nov 1, 2026math.NTscore 0

For the powerful part Q_2(m) of m, this formalization proves that limsup Q_2(n(n+1)...(n+l))/n^2 is infinite for every l >= 2 (the second question of Erdős Problem 935), and at least 1 for every l >= 1 (a consequence of a result of Mahler noted by Erdős). Both use solutions of the Pell equation x^2 = 8y^2 + 1.

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