AIME I Problem 1 2007

[zefuri]

How many positive perfect squares less than 10^{6} are multiples of 24?

[stupidityismygam]

since it is a perfect square then it has to have multiple of 2 exponents in its prime factorization

so 24=3*2^3
so the square has to be 3^2*2^4 or the number has to be from 1 to 1000, and a multiple of 12 (taking the square root of the number and the range)

so [unparseable or potentially dangerous latex formula] so the answer is [unparseable or potentially dangerous latex formula]

[AuSmith]

Or rather, if a square of a number is less than [unparseable or potentially dangerous latex formula], then the number is less than [unparseable or potentially dangerous latex formula] ([unparseable or potentially dangerous latex formula] is an increasing function for [unparseable or potentially dangerous latex formula]). Then, like he said, [unparseable or potentially dangerous latex formula], and if [unparseable or potentially dangerous latex formula], then [unparseable or potentially dangerous latex formula]. Further iff [unparseable or potentially dangerous latex formula] will [unparseable or potentially dangerous latex formula]... then such n are from the set [unparseable or potentially dangerous latex formula].