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