Y by langkhach11112, Davi-8191, HamstPan38825, HWenslawski, megarnie, Adventure10, Mango247, ehuseyinyigit, ys-lg, and 1 other user
For a prime
, a subset
of residues modulo
is called a sum-free multiplicative subgroup of
if
there is a nonzero residue
modulo
such that
(all considered mod
), and
there are no
(not necessarily distinct) such that
.
Prove that for every integer
, there is a prime
and a sum-free multiplicative subgroup
of
such that
.
Proposed by Noga Alon and Jean Bourgain












Prove that for every integer





Proposed by Noga Alon and Jean Bourgain