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Complete Solution of a Problem of Diophantus and Euler
Author(s) -
Dujella Andrej,
Fuchs Clemens
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461070400609x
Subject(s) - euler's formula , mathematics , property (philosophy) , set (abstract data type) , product (mathematics) , square (algebra) , square number , pure mathematics , combinatorics , mathematical analysis , computer science , geometry , philosophy , epistemology , programming language
It is proved that there does not exist a set of four positive integers with the property that the product of any two of its distinct elements plus their sum is a perfect square. This settles an old problem investigated by Diophantus and Euler.