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For questions about sequences of integers. References are often made to the online resource oeis.org.

9 votes

Consecutive numbers with mutually distinct exponents in their canonical prime factorization

We prove that there are only finitely many such intervals. Suppose $[36n + 7, 36n + 29]$ is one such interval. Now, $36n + 10$ and $36n + 15$ cannot both be divisible by $5$ (since one must occur …
Adam P. Goucher's user avatar
47 votes
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Can we find lattice polyhedra with faces of area 1,2,3,...?

I found a 32-face example with face areas $\{ 1, 2, \dots, 32 \}$: It took a reasonable amount of experimentation to stop it from self-intersecting.
Adam P. Goucher's user avatar