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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
6
votes
Values of the determinants $\det[(j-k)^m+\delta_{jk}]_{1\le j,k\le n}\ (m=1,2,3,\ldots)$
Edited to give a more complete (and cleaner) answer valid for all $m, n$. My original answer only applied for $n \geq m+1$, and only went through the proof for the case of $(x-y)^m$.
Say we have a pol …