MathDB

Let

p

be an odd prime. An integer

x

is called a quadratic non-residue if

p

does not divide

x-t^2

for any integer

t

. Denote by

A

the set of all integers

a

such that

1\le a<p

, and both

a

and

4-a

are quadratic non-residues. Calculate the remainder when the product of the elements of

A

is divided by

p

.
Proposed by Richard Stong and Toni Bluher

Problem Statement