Abstract
Alon, Angel, Benjamini and Lubetzky [1] 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
