MathDB

A well-known theorem asserts that a prime

p > 2

can be written as the sum of two perfect squares (

p = m^2 +n^2

, with

m

and

n

integers) if and only if

p \equiv 1

(mod

4

). Assuming this result, find which primes

p > 2

can be written in each of the following forms, using integers

x

and

y

: a)

x^2 +16y^2,

4x^2 +4xy+ 5y^2.

A3