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Euler’s Partition Theorem

Karol Pąk (2015)

Formalized Mathematics

In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1]). Euler’s Partition Theorem is listed as item #45 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/ [27].

Exceptional sets in Waring's problem: two squares and s biquadrates

Lilu Zhao (2014)

Acta Arithmetica

Let R s ( n ) denote the number of representations of the positive number n as the sum of two squares and s biquadrates. When s = 3 or 4, it is established that the anticipated asymptotic formula for R s ( n ) holds for all n X with at most O ( X ( 9 - 2 s ) / 8 + ε ) exceptions.

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