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# Questions

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### Teaching statements for math jobs?

nov 30 09 at 20:31 Deane Yang 12.6k13380

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### Why are powers of $\exp(\pi\sqrt{163})$ almost integers?

may 18 at 9:12 Didier Piau 4,19311015

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### Is there a combinatorial reason that the (-1)st Catalan number is -1/2?

feb 19 10 at 3:39 Jacques Carette 6,68711435

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### If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4. Is there a “nice” proof of this fact?

mar 22 at 18:21 Shaswata 1

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### What relationship, if any, is there between the diameter of the Cayley graph and the average distance between group elements?

apr 13 11 at 5:37 Denis Chaperon de LauziÃ¨res 2,19428

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### When are some products of gamma functions algebraic numbers?

dec 3 09 at 21:18 Felipe Voloch 16.6k23661

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### What’s the probability that k + n^2 is squarefree, for fixed k?

mar 1 10 at 22:53 Bjorn Poonen 14.2k24775

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### How many pairs (M, N) of sets of size n have M + N = {0, 1, …, n^2-1}?

apr 8 10 at 13:47 D. Savitt 1,8911518

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### How can I generate random permutations of [n] with k cycles, where k is much larger than log n?

jun 3 10 at 23:15 James Martin 1,596414

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### An integral that somehow equals pi^2/6 and involves dilogarithms?

apr 5 11 at 2:47 Tom Dickens 69348