Difference between revisions of "1987 USAMO Problems/Problem 1"
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Revision as of 20:57, 10 April 2018
Find all solutions to , where m and n are non-zero integers.
Expanding both sides, Note that can be canceled and as , can be factored out. Writing this as a quadratic equation in : . The discriminant equals , which we want to be a perfect square. Miraculously, this factors as . This is square iff is square. It can be checked that the only nonzero that work are . Finally, plugging this in and discarding extraneous roots gives all possible ordered pairs as .
|1987 USAMO (Problems • Resources)|
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|All USAMO Problems and Solutions|