MathDB

(254) 2

Part of 1990 Tournament Of Towns

Problems(1)

TOT 254 1990 Spring O S2 n =4k+1 , exist n odds whose sum = product

Source:

6/8/2024
Prove that (a) if the natural number nn can be represented as n=4k+1n =4k+1 (where kk is an integer), then there exist nn odd positive integers whose sum is equal to their product, (b) if nn cannot be represented in this form then such a set does not exist.
(M. Kontsevich)
number theory