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arXiv · 2608.08019

Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures

Debmalya Basak·Anji Dong·Katerina Saettone·Alexandru Zaharescu
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Abstract

On the occasion of George Andrews' and Bruce Berndt's combined 170th birthday, we prove two conjectures of Sir Frederick Pollock that are more than 170 years old. In 1843, Pollock conjectured that every positive integer is the sum of at most 13 icosahedral numbers, or at most 21 dodecahedral numbers. We establish refined versions of both conjectures.

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Debmalya Basak, Anji Dong, Katerina Saettone, Alexandru Zaharescu. 2026-08-08. Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures. https://doi.org/10.1093/imrn%2Frnaf180

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