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Seminar

# K-multimagic squares and magic squares of kth powers via the circle method.

Speaker

Daniel Flores (Purdue)

Date

Wed, Nov 20 2024, 1:00pm

Location

383N

*K-multimagic squares* of order N, these are N × N magic squares which remain magic after raising each element to the kth power for all 2 ⩽ k ⩽ K. Given K ⩾ 2, we consider the problem of establishing the smallest integer N(K) for which there exists *non-trivial* K-multimagic squares of order N(K). Previous results on multimagic squares show that N(K) ⩽ (4K − 2)^K for large K. Here we utilize the Hardy-Littlewood circle method and establish the bound N_2(K) ⩽ 2K(K + 1) + 1. We additionally address the simpler problem of magic squares consisting of kth powers, improving on a recent result by Rome and Yamagishi.