Is there a relationship between odd composite numbers and their factors?

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SUMMARY

The discussion establishes a mathematical relationship involving odd composite numbers and their factors. Specifically, for any odd composite number 'N', if 'u' is defined as (N-1)/2 and 'v' as u+1, then the condition u^2(mod p) = v^2(mod p) holds true if and only if 'p' is a factor of 'N'. This property highlights a direct connection between the modular arithmetic of the derived values and the factors of the original odd composite number.

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yourskadhir
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Hi,

For any odd composite 'N', let u = (N-1)/2, v = u+1, then u^2(mod p) = v^2(mod p) if and only if 'p' is a factor of 'N'.

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Hi, Kadhirvel,
it's a bit of a trivial property, isn't it? You are saying that 2u+1 ≡ 0 (mod p), after you cancel u^2 from both sides. But 2u+1 was the same as N from the beginning.
 

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