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- W4366999260 abstract "For given positive integers $m$ and $n$ with $m<n$, the Prouhet-Tarry-Escott problem asks if there exist two disjoint multisets of integers of size $n$ having identical $k$th moments for $1leq kleq m$; in the ideal case one requires $m=n-1$, which is maximal. We describe some searches for ideal solutions to the Prouhet-Tarry-Escott problem, especially solutions possessing a particular symmetry, both over $mathbb{Z}$ and over the ring of integers of several imaginary quadratic number fields. Over $mathbb{Z}$, we significantly extend searches for symmetric ideal solutions at sizes $9$, $10$, $11$, and $12$, and we conduct extensive searches for the first time at larger sizes up to $16$. For the quadratic number field case, we find new ideal solutions of sizes $10$ and $12$ in the Gaussian integers, of size $9$ in $mathbb{Z}[isqrt{2}]$, and of sizes $9$ and $12$ in the Eisenstein integers." @default.
- W4366999260 created "2023-04-27" @default.
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- W4366999260 date "2023-04-21" @default.
- W4366999260 modified "2023-10-18" @default.
- W4366999260 title "Ideal solutions in the Prouhet-Tarry-Escott problem" @default.
- W4366999260 doi "https://doi.org/10.48550/arxiv.2304.11254" @default.
- W4366999260 hasPublicationYear "2023" @default.
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