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THE UNIQUENESS OF THE PRIME MARKOFF NUMBERS

Published online by Cambridge University Press:  01 August 1998

J. O. BUTTON
J. O. BUTTON
Affiliation:
Wadham College, Oxford OX1 3PN
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Abstract

Given the Diophantine equation a2+b2+c2=3abc, a solution triple of natural numbers (a, b, c) can be arranged in ascending order so that a[les ]b[les ]c. Then, given the largest element c, one can ask whether this uniquely determines the triple. This is referred to as the Markoff conjecture. The paper proves that, if c is prime, then there is indeed only one triple that solves the equation with c as the largest element. The proof uses only standard algebraic number theory, but it was prompted by geometric considerations.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 9 - 17
Copyright
The London Mathematical Society 1998

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