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On the Unicity Conjecture for Markoff Numbers

Published online by Cambridge University Press:  20 November 2018

Arthur Baragar
Arthur Baragar*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, e-mail:, [email protected]
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Abstract

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In 1913 Frobenius conjectured that for any positive integer m, there exists at most one pair of integers (x, y) with 0 ≤ x ≤ y ≤ m such that (x, y, m) is a solution to the Markoff equation: x2 + y2 + m2 = 3xym. We show this is true if either m, 3m — 2 or 3m + 2 is prime, twice a prime or four times a prime.

Keywords

11D25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 3 - 9
Copyright
Copyright © Canadian Mathematical Society 1995

References

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