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Could anybody tell me if there's a method which checks if the number n is a prime? I know only an algo O(sqrt(n)) which is well-know. There's Eratostenes' Sieve too, but the big numbers cannot be checked due to memory limits.

Hi Dreamer!
In my opinion your input are wrong because there doesn't exist such integer that a+b=2 and a*b=2.

If you tried solving those equations you would be given:
a*(2-a)=2
-a^2 + 2a - 2 = 0

delta = 4-4*(-1)*2 = -4 <0 => there is no integer a.

Or maybe I misunderstood everything... Anyway, I ...

Could anybody give some critical test cases to this problem?
Thanks.

Why answer for this test is Impossible? Could anybody explain me that?
And one more thing...why the answer for this test case: is 80?

When rejudge are going to be finished?