Can someone explain me why isn't dividable with 125?

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- Feb 7th 2006, 08:09 AMDenMac21Explanation
Can someone explain me why isn't dividable with 125?

- Feb 7th 2006, 09:52 AMCaptainBlackQuote:

Originally Posted by**DenMac21**

. You will find

is never divisible by and so cannot be divisible by .

RonL - Feb 7th 2006, 02:55 PMThePerfectHackerQuote:

Originally Posted by**DenMac21**

Noticing that 5 is a prime, look at its discrimanant ( .

The above congruence has a solution if and only if its discrimant is a quadradic residue.

Since .

Apply Euler's Criterion to determine if something is a quadradic residue we get that,

Thus, is never divisible by 5, thus how can it be divisible by ?

Thus, we have shown it is impossible.

Q.E.D.

To remind you Euler's Criterion states, is a quadradic residue of if and only if,