Disprove with the counter example: If a^2 = b^2 (mod n) then a=b (mod n)..
where "=" means the equivalence.
I think...since, n\a^2 - b^2...proceeds to n\(a-b)(a+b)...shows that n also divides (a-b)...so can't we directly say that a=b (mod n)..??
how do I do this one?
Thanks for any help!
I got until this part:
n divides a^2 - b^2 then we could say for some k, (a-b)(a+b) = nk..now similarly for some l , a+b = nl..
so dividing both of these equations we get: (a-b) = k/l...and I am stuck after this part! is this a right way to proceed??
well I tried disproving it and got this one. Like you said, just need one example where ti does not work...
For example, a = 7, b = 2, N = 3.
7^2 mod 3 = 1
2^2 mod 3 = 1
so 7^2 mod 3 = 2^2 mod 3
7 mod 3 = 1
2 mod 3 = 2
so 7 mod 3 != 2 mod 3
So it satisfies our counterexample....but I still don't understand, how do we know that any conditions like this one, proves or disproves? so do we always look for disproving first and pick any examples where it does not work. Or something else?