Hello, ride12!

given: .

Prove that you can eliminate one factor so that the remaining number is a perfect square.

Consider the frequency of each factor in the number

The odd factors {1, 3, 5, ... , 99} all appear anevennumber of times.

. . They will comprise a square number.

The even factors {2, 4, 6, ..., 100} all appear anoddnumber of times.

. . If we eliminateone of each, the rest will comprise a square number.

But

So we can eliminate just

. . and leave the , a square.

Then: . . . . a square