(strong) induction proof:$\left(a+\sqrt{b}\right)^n+\left(a-\sqrt{b}\right)^n=2k,a,b,k\in\mathbb N, a>b$
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The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer
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If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$
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Prove by induction that a^n+a^-n is an integer.
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Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
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Proof by Induction that $3^n ≥ 1+2^n$
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Prove by induction. $n \in \mathbb N$.
138683
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction
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Proving by induction $4^n  0$
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Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
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Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
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How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?
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Proof by induction - is this correct?
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Proving this inequality by mathematical induction
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Induction proof of lower bound for $\sum \sqrt n$
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Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
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Prove $(ah,bk)=(a,b)(h,k)\left(\frac{a}{(a,b)},\frac{k}{(h,k)}\right)\left(\frac{b}{(a,b)},\frac{h}{(h,k)}\right)$
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Need help with Proof by Strong Induction question