1998 JBMO Problems/Problem 1
Prove that the number (which has 1997 of 1-s and 1998 of 2-s) is a perfect square.
The number can be rewritten as This number has a few geometric series and can be written as Simplifying results in Notice that and That means we can "factor" the numerator, and doing so results in Since is divisible by 3, we conclude that the number is a perfect square.
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