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divisible in primes

Source: Mathematics Regional Olympiad of Mexico Southeast 2017 P3

October 24, 2021

number theory

Problem Statement

Let

p

of prime of the form

3k+2

such that

a^2+ab+b^2

is divisible by

p

for some integers

a

and

b

. Prove that both of

a

and

b

are divisible by

p