1

Part of 1990 Kurschak Competition

Problems(1)

Divisor d of pn^2, such that n^2+d is a square

Source: Kürschák 1990, problem 1

p>2

be a prime number and

n

a positive integer. Prove that

pn^2

has at most one positive divisor

d

n^2+d

is a square number.

modular arithmeticnumber theoryrelatively primenumber theory unsolved