Sumsets being squares (CROSBI ID 194057)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
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