MathDB

Assume that the following generating function equation is correct, prove the following statement:

\Pi_{i=1}^{\infty} (1+x^{3i})\Pi_{j=1}^{\infty} (1-x^{6j+3})=1

Statement: The number of partitions of

n

to numbers not of the form

6k+1

6k-1

is equal to the number of partitions of

n

in which each summand appears at least twice. (10 points) Proposed by Morteza Saghafian

Problem Statement