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Expositio paper exp-20261001-98d2cb

The pentagonal number theorem

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In this note, we discuss Euler's proof of the pentagonal number theorem and his related work on the subject. We also give Franklin's combinatorial proof as well as several problems that extend the results discussed in the note.

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exp-20261001-98d2cbv1 Latest public version Public since October 1, 2026 Submitted October 1, 2026 0 saves
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Simon Rubinstein-Salzedo (Kaleidoscope Circles)

Abstract

In this note, we discuss Euler's proof of the pentagonal number theorem and his related work on the subject. We also give Franklin's combinatorial proof as well as several problems that extend the results discussed in the note.

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Mathematics
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History and biography History of mathematics and mathematicians History of mathematics in the 18th century
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Combinatorics Enumerative combinatorics Combinatorial aspects of partitions of integers

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exp-20261001-98d2cbv1

The pentagonal number theorem

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Uploaded Oct 1, 2026 276817 bytes Selected Latest
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