The following problem was posed by Erdös and Graham (and is listed as problem #437 on the Erdös problems website): Problem 1 Let be integers. How many of the partial products , , , can be squares? Is it true that, for any , there can be more than squares? If one lets denote the […]
Many modern mathematical proofs are a combination of conceptual arguments and technical calculations. There is something of a tradeoff between the two: one can add more conceptual arguments to try to reduce the technical computations, or vice versa. (Among other things, this leads to a Berkson paradox-like phenomenon in which a negative correlation can be […]