# Tagged Questions

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### Prove that if $n^{2} - \left(n - 2\right)^{2}$ is not divisible by $8$ then $n$ is even

Let n be an integer. Prove that if $n^{2} -\left(n - 2\right)^{2}$ is not divisible by $8$ then $n$ is even. Can anyone help me step by step to understand this.
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### Prove that if $3|(a^2+b^2)$, then $3|a$ and $3|b$, where $a, b$ are integers [duplicate]

I would like to know how to prove the above statement by contradition. Somebody said that one should prove it by this method but I have no idea what it is.
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### Prove the limit..

$\varinjlim \sqrt{n^2+1}-n=0$. I need to prove that this converges to 0. Usung the definition of a sequence helps for the normal problems but for this I believe the triangle inequality is used at ...
377 views

### Proof By Contradiction, Rational Roots

This was an exam question that I got totally wrong and am a bit question. Prove $x^3 + x + 1 = 0$ has no solutions. Prove by contradiction. Assume: $x^3 +x +1 =0$ has at least one rational root. ...
### Prove that if $(m - 1)! + 1$ is divisible by $m$, $m$ is a prime with $(m - 1)! = 1.2.3…(m - 2)(m - 1)$
$m$ is a positive integer, and $m > 1$, Prove that if $(m - 1)! + 1$ is divisible by $m$, $m$ is a prime. Solve this by making a contradiction. My english isn't so well. Please help and thank you ...