Difference between revisions of "2013 JBMO Problems/Problem 1"
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Revision as of 21:49, 18 January 2019
Problem
Find all ordered pairs of positive integers for which the numbers and are both positive integers
Solution
Adding to both the given numbers we get:
is also a positive integer so we have:
= is a positive integer
Similarly,
is also a positive integer so we have:
= is a positive integer
Combining above results we get:
which is a valid solution.
which are valid solutions.
Thus, all solutions are: