Number Theory

Let $m$ and $n$ be non-negative integers. If $m = 6n + 2$, then what integer between $0$ and $m$ is... Let $a$, $b$, and $c$ be integers such that $a \equiv 1 \pmod{7}$, $b \equiv 2 \pmod{7}$, and $c \eq... For a certain positive integer $n$, the number $n^{6873}$ leaves a remainder of $3$ when divided by... Find the number of $7$-digit numbers, where the sum of the digits is divisible by $11.$ Find the remainder when $1! + 2! + 3! + \dots + 100!$ is divided by $2$. Find the largest positive integer $n$ such that \[\frac{(n + 1)^2}{n + 2}\] is an integer. What is the largest integer $n$ such that $11^n$ divides $1,000,000!$ ? The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$ What is th... Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $11.$ When t... let a be a rational number and b be an irrational number. Which of the following statements are true...