Confusion?

Number Theory Level 3

Given:

$p$ , $x$ , and $y$ are positive integers.
$p$ can be expressed as $p=x^2+y^2$
$p-1$ is divisible by $4$

What can you conclude from here?

Not enough information

p

may be prime or composit

p

is prime

1 solution

Chew-Seong Cheong
Feb 13, 2020

When $x=1$ and $y=2$ , then $p = 5$ , a prime, and $p-1 = 4$ divisible by $4$ . When $x=3$ and $y=4$ , then $p = 25$ , a composite, and $p-1 = 24$ divisible by $4$ . Therefore $p$ may be prime or composite.

Confusion?

1 solution

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