7

Part of 2018 Ukraine Team Selection Test

Problems(1)

pn^2 has no more than one divisor d such that n^2+d is perfect square

Source: Ukraine TST 2018 p7

The prime number

p > 2

and the integer

n

are given. Prove that the number

pn^2

has no more than one divisor

d

n^2+d

is the square of the natural number. .

Perfect Squarenumber theoryprimedivisor