Number Theory
# Prime Factorization and Divisors

\[\Huge \frac{\color{blue}{50!}}{\color{red}{51}}\]

What is the remainder of the division above?

Let \(Y = n(n+1) \) for some positive integer \(n\). Which of the following statements is true?

How many perfect squares are there between \(101\) and \(9999\)?

Find the sum of the digits of \(\large 2^{2999} × 5^{3002}\) when multiplied out.

Find the smallest positive integer which is both a perfect square and a perfect cube.

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