Hi, I'm looking for some references to the problem of minimizing products of the form \prod_{j=0 \neq k}^d |b^k - b^j| where k is chosen between 0 and j, for a fixed base b. It looks like, for sufficiently large b > 1, minimizing this product requires choosing k = d, unless b gets close to 1 in which case eventually k must be chosen to be e.g. floor(d/2). If 0 < b < 1, the reverse process occurs: k must be chosen to be 0, unless b is really close to 1 in which case k must become e.g. floor(d/2). I'd like to believe there's literature on this subject, however searching for things like "minimize the product of differences of powers" returns material that is only related to the search query by the fact that the terms appear in the search results. Looking at the expression with Wolfram, like this, https://www.wolframalpha.com/input/?i=%5Cprod_%7Bj%3D0%7D%5Ed+%28b%5Ek+-+b%5... returns a reference to the q-Pochhammer symbol. Digging through that, I was not able to immediately find a way to minimize the product or show which factor has to be removed from the product. I also tried making b = e, applying ln to the product, then approximating the sum by the integral. The resulting integral (courtesy of Wolfram Alpha) relies on Spence's dilogarithm function Li_2. After some approximations evaluating the integral, it looks like the product as a whole is about e^O(d). However, I do not immediately see how to minimize the product by choice of k depending on b. Do you have any suggestions on where to look? TIA! Andres.