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• 94 Why does cancelling change this equation?
• 37 101102103104105106..............149150? What is the remainder when divided by 9?
• 18 Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
• 14 What are "desires of the flesh"?
• 11 How to prove that for $a_{n+1}=\frac{a_n}{n} + \frac{n}{a_n}$ , we have $\lfloor a_n^2 \rfloor = n$?
• 9 Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another.
• 8 If $\sum_n^\infty a_n$ diverges such that $a_n$ converges to 0. Prove that there exists a subsequence of $a_n$ such that $\sum_k a_{n_k}$ converges.
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