Random article ( of 1126 ) Latest updates

User Tools

Site Tools


content / mathematics / newman_conjecture

Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

The Newman conjecture

The Newman conjecture was created by Morris Newman in 1960. It remains unsolved.

It's stated formally as :

For any integers m and r such that $${\displaystyle 0\leq r\leq m-1}$$the value of the partition function $${\displaystyle p(n)}$$ satisfies the congruence $${\displaystyle p(n)\equiv r{\pmod {m}}}$$ for infinitely many non-negative integers n.

In plain language :

Given arbitrary m, r, are there infinitely values of n such that the partition function at n is congruent to r mod m?

See : Periodicity Modulo m and Divisibility Properties of the Partition Function Transactions of the American Mathematical Society, Vol. 97, No. 2 pp. 225-236

And Wikipedia

THIS WEBSITE DOES NOT USE TRACKING, ADVERTISING, OR ANALYTICAL COOKIES OF ANY KIND.
All essential cookies (for login status etc) are automatically deleted at the end of the session.
(full details here)

Show another (random) article

Suggestions for corrections and ideas for articles are welcomed : Get in touch!


Further resources :