1.To prove - For any natural number n, the number N is not divisible by 3 2. N = n2+1 3. Dividing naturals into three classes according to remainder outcomes during division by 3 ie. 0,1,2 ; for any whole number k ---> 3k, 3k+1, 3k+2 And then substitute the values respectively to derive a 'false' inference from the equation. I want to know whether this is the only standard method of proving such divisibility equations true or false ; or is there any other way out?