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Bart Michels
Some answers I am proud of:
- Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
- Hat 'trick': Can one of them guess right?
- Elementary proof of Zsigmondy's theorem
- Proving $\sum_{k=0}^n{2k\choose k}{2n-2k\choose n-k}=4^n$ (combinatorial proof)
- Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$ (funny proof)
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