If is an integer, then for every residue class (mod ), there are infinitely many nonnegative integers for which , where is the partition function P.
Newman's Conjecture
See also
Erdős-Ivić Conjecture, Partition Function PExplore with Wolfram|Alpha
References
Newman, M. "Periodicity Modulo and Divisibility Properties of the Partition Function." Trans. Amer. Math. Soc. 97, 225-236, 1960.Ono, K. "Distribution of the Partition Functions Modulo ." Ann. Math. 151, 293-307, 2000.Referenced on Wolfram|Alpha
Newman's ConjectureCite this as:
Weisstein, Eric W. "Newman's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NewmansConjecture.html