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This is an extract from Apéry's biography (which some of the people have already enjoyed in this answer). During a mathematician's dinner in Kingston, Canada, in 1979, the conversation turned ...

In Finite Mathematics by Lial et al. (10th ed.), problem 8.3.34 says: On National Public Radio, the Weekend Edition program posed the following probability problem: Given a certain number of ...

Let's define non-trivial binomial coefficients as values of $\binom{n}{k}$, where $n$ and $k$ are positive integers such that $2 \le k \le \frac{n}{2}$. (Therefore, $6$ is the smallest non-trivial ...

This question leads to a follow-up: are there any Eisenstein triples (satisfying $a^2\pm ab+b^2=c^2$) in one row of Pascal's triangle apart from the following: $\binom{23}{8}^2+\binom{23}{8}\binom{23}{...

I want to know the exact number of non-negative integer solutions of $a_1 + 2a_2 + \ldots + k \cdot a_k = n$. I know that it is the co-efficient of $x^n$ in $(1 - x^{a_1})^{-1} \cdot (1 - x^{a_2})^{-...