Thread: Number theory(Primes)

*Determine whether the following assertions are true or false. if true, prove the result, and if false, give a counter example

2. If p is a prime and p/(a^2+b^2) and p/(b^2+c^2) then p/(a^2-c^2).

Hint : if then

oh bruno, i don't really get it..can u help me

If then . Then , so .

Now how can you get from and ?

i'm still blurred...sorry i still don't get it. oh..is it true? is it the final answer or do i need to elaborate it further?

Exactly one minute has gone by between my post and your call for more help. Perhaps taking five minutes to try to understand wouldn't do any harm.

If you can't even judge by yourself whether this is the answer or not, you might want to go back to your textbook. Do you even understand the statement of the problem?

Maybe this will help:

We will use some substitution, let and

So we have and

Note that , so we are trying to see if

In case Bruno's proof confused you because he used and also, I'll put it here again with different letters, and with abit more detail.

If and then there exists and such that and . So .

Note that the just means that it works for both addition and subtraction.

Now, is just an integer, which we can designate as . So, . Since exists, by definition

What Bruno is asking is that if we let and , is there a way we can add or subtract or so that we get