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Number Theory, Fermat's Theorm

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Let p and q be prime number greater than 3. Prove that 24|p^2-q^2

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Solution Summary

The proof to the statement " Let p and q be prime number greater than 3. Prove that 24|p^2-q^2" is given using Fermat's Theorem in such a way that the students can easily understand and use the method explained for other problems also.

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Let p and q be prime number greater than 3. Prove that 24|p^2-q^2

Solution :

Let p and q be two odd primes greater than 3.

Since p is a prime greater than 3, therefore, (p , 1) = 1
Also 3 is prime.

By Fermat Theorem, p2  1 mod 3 ........................(1)

Similarly, q2  1 mod 3 ...

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