Positive Integers (a 2 + b 2)/(ab + 1) are Squares

Jens-P. Bode and Heiko Harborth

A chapter in Applications of Fibonacci Numbers, 2004, pp 63-67 from Springer

Abstract: Abstract In 1988, the International Mathematical Olympiad (IMO) was held in Canberra and on day II the following Problem 6 was posed (see [1,2]): Let a and b be positive integers such that ab + 1 divides a 2 + b 2. Show that (a 2 + b 2)/(ab + 1) is the square of an integer.

Keywords: 11B37; 11D09; 39A05 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-306-48517-6_8

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