prove that if n is a perfect square, then n+2 is not a perfect square.
I approached this way:
hypothesis: n+2=k^2
conclusion: n=k;
But i tried both direct and indirect proof, but neither works. Or my approach is not right? pls help
prove that if n is a perfect square, then n+2 is not a perfect square.
I approached this way:
hypothesis: n+2=k^2
conclusion: n=k;
But i tried both direct and indirect proof, but neither works. Or my approach is not right? pls help
Hello, zpwnchen!
Prove that if is a perfect square, then is not a perfect square.
is a perfect square: .
Suppose is a perfect square: .
We have: .
Then: .
We have a system of equations: .
. . which has the solution: .
But are integers . . . We have reached a contradiction.
Therefore. is not a perfect square.