Difference between revisions of "2015 USAMO Problems/Problem 2"
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Revision as of 02:56, 12 May 2015
Problem
Solve in integers the equation
Solution
We first notice that both sides must be integers, so must be an integer.
We can therefore perform the substitution where is an integer.
Then:
is therefore a perfect square and can be replaced with
By substituting using we get:
or
Using substitution we get the solutions: