Can p be an odd prime that divides both r^2-s^2 and r^2+s^2?

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The discussion centers on the mathematical proof regarding the greatest common divisor (gcd) of the expressions r² - s² and r² + s², given that gcd(r, s) = 1. It is established that if p is an odd prime dividing both expressions, it leads to a contradiction, thereby proving that gcd(r² - s², r² + s²) must equal either 1 or 2. This conclusion is critical for understanding the properties of prime divisors in relation to these specific polynomial forms.

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Can anyone help me with this?

If gcd(r,s)=1 then prove that gcd(r^2-s^2, r^2+s^2)=1 or 2.

i'm so confused.
 
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Let p be an odd prime that divides both r^2-s^2 and r^2+s^2. Show that this leads to a contradiction.
 

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