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Sumsets being squares (CROSBI ID 194057)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Dujella, Andrej ; Elsholtz, Christian Sumsets being squares // Acta mathematica Hungarica, 141 (2013), 4; 353-357. doi: 10.1007/s10474-013-0334-8

Podaci o odgovornosti

Dujella, Andrej ; Elsholtz, Christian

engleski

Sumsets being squares

Alon, Angel, Benjamini and Lubetzky recently studied an old problem of Euler on sumsets for which all elements of A + B are integer squares. Improving their result we prove: 1. There exists a set A of 3 positive integers and a corresponding set B ⊂ [0, N] with |B| ≫ (logN)^(15/17), such that all elements of A + B are perfect squares. 2. There exists a set A of 3 integers and a corresponding set B ⊂ [0, N] with |B| ≫ (logN)^(9/11), such that all elements of the sets A, B and A + B are perfect squares. The proofs make use of suitably constructed elliptic curves of high rank.

sumsets ; squares ; elliptic curves of high rank

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Podaci o izdanju

141 (4)

2013.

353-357

objavljeno

0236-5294

1588-2632

10.1007/s10474-013-0334-8

Povezanost rada

Matematika

Poveznice
Indeksiranost