1

Part of 2018 Argentina National Olympiad

Problems(1)

r= p mod 210, r =a^2+b^2

Source: 2018 Argentina OMA Finals L3 p1

p

a prime number and

r

the remainder of the division of

p

210

. It is known that

r

is a composite number and can be written as the sum of two non-zero perfect squares. Find all primes less than

2018

that satisfy these conditions.

number theoryremainder