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

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- September 13th 2009, 06:04 PMzpwnchenhelp me solve this problem
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 - September 13th 2009, 08:02 PMSoroban
Hello, zpwnchen!

Quote:

Prove that if is a perfect square, then isa perfect square.*not*

is a perfect square: .

Supposea perfect square: .*is*

We have: .

Then: .

We have a system of equations: .

. . which has the solution: .

But are integers . . . We have reached a contradiction.

Therefore. isa perfect square.*not*

- September 14th 2009, 07:20 AMzpwnchen
Thank you so much!

Can we say that n=a^2 where a is 1/2. therefore, n is not a perfect. we reached a contradiction?

Can we use direct or indirect proof for it?