MathDB

All the positive integer that can write in form a^2+2b^2

Source: Romania TST 1997

October 10, 2005

modular arithmeticnumber theory solvednumber theoryDivisibilityMultiplicative NTMultiplicative order

Problem Statement

Suppose that

A

be the set of all positive integer that can write in form

a^2+2b^2

(where

a,b\in\mathbb {Z}

and

b

is not equal to

0

). Show that if

p

be a prime number and

p^2\in A

then

p\in A

.
Marcel Tena