Difference between revisions of "2005 JBMO Problems/Problem 1"
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Revision as of 01:55, 23 December 2018
Problem 1
Find all positive integers satisfying the equation
Solution
We can re-write the equation as:
or
The above equation tells us that is a perfect square. Since . this implies that
Trying all values of from to , we find that result in perfect squares.
Thus, we have cases to check:
Thus all solutions are and .