Abstract
Euler proves that the infinite product s=(1-x)(1-x^2)(1-x^3)... expands into
the power series s=1-x-x^2+x^5+x^7-..., in which the signs alternate in two's
and the exponents are the pentagonal numbers. Euler uses this to prove his
pentagonal number theorem, a recurrence relation for the sum of divisors of a
positive integer.
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