The 2-adic valuation of an integer n is the exponent of the highest power of 2 that divides n and is denoted by \(\nu _2(n)\) . In this paper, we prove that Euler’s partition function p(n) can be expressed in terms of \(\nu _2(n)\) . Our approach allows us to express the sum of positive divisors of n in terms of \(\nu _2(n)\) . We introduce the notion of 2-adic color partition and provide a new combinatorial interpretation for Euler partition function p(n). Connections between partitions and the game of m-Modular Nim with two heaps are presented in this context.
