2023 USAJMO Problems/Problem 1
Problem
Find all triples of positive integers that satisfy the equation
Solution 1
We claim that the only solutions are and its permutations.
Factoring the above squares and canceling the terms gives you:
Jumping on the coefficients in front of the ,
,
terms, we factor into:
Realizing that the only factors of 2023 that could be expressed as are
,
, and
, we simply find that the only solutions are
by inspection.
-FFAmplify
Alternatively, a more obvious factorization is:
Proceed as above.