This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 3

2008 AIME Problems, 15
Tags: number theory , modular arithmetic , intermediate number theory
Find the largest integer $ n$ satisfying the following conditions: (i) $ n^2$ can be expressed as the difference of two consecutive cubes; (ii) $ 2n\plus{}79$ is a perfect square.

2008 AIME Problems, 7
Tags: number theory , intermediate number theory , inequalities
Let $ S_i$ be the set of all integers $ n$ such that $ 100i\leq n < 100(i \plus{} 1)$. For example, $ S_4$ is the set $ {400,401,402,\ldots,499}$. How many of the sets $ S_0, S_1, S_2, \ldots, S_{999}$ do not contain a perfect square?

2017 AIME Problems, 9
Tags: number theory , intermediate number theory
Let $a_{10} = 10$, and for each integer $n >10$ let $a_n = 100a_{n - 1} + n$. Find the least $n > 10$ such that $a_n$ is a multiple of $99$.