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Integral solutions of ass and mule problems

Published online by Cambridge University Press:  01 August 2016

David Singmaster
David Singmaster*
Affiliation:
87 Rodenhurst Road, London SW4 8AF, e-mail:zingmast@lsbu.ac.uk
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Extract

In [1], Tomislav Došlić studies a special case of the classic Ass and Mule Problem and determines when integral data give integral solutions. The question of when integral data gives integral solutions in the general case intrigued me some years ago; I even published the assertion that I could not see any simpler result than computing the answers and seeing if the results were integral [2]. However, I later found a satisfactory result for this and some variants of the problem, which are given in [3, 4]. Here I give this result, which describes an infinite set, and show it leads to a simpler derivation of Došlić's interesting result that his variation has only 16 positive integral solutions. A different method permits finding the nonpositive integral solutions. I will then state a similar but unsolved problem.

Type
Articles
Information
The Mathematical Gazette , Volume 89 , Issue 516 , November 2005 , pp. 365 - 370
Copyright
Copyright © The Mathematical Association 2004

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References

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