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Newest Number Theory Questions

1. Let $m$ and $n$ be non-negative integers. If $m = 6n + 2$, then what integer between $0$ and $m$ is the inverse of $5$ modulo
   1. 1 answer
   2. asked by Lily
   3. 163 views
2. Let $a$, $b$, and $c$ be integers such that $a \equiv 1 \pmod{7}$, $b \equiv 2 \pmod{7}$, and $c \equiv 6 \pmod{7}$. What is the
   1. 1 answer
   2. asked by Jane
   3. 163 views
3. For a certain positive integer $n$, the number $n^{6873}$ leaves a remainder of $3$ when divided by $23.$ What remainder does
   1. 1 answer
   2. asked by Lily
   3. 176 views
4. Find the number of $7$-digit numbers, where the sum of the digits is divisible by $11.$
   1. 1 answer
   2. asked by Lily
   3. 169 views
5. Find the remainder when $1! + 2! + 3! + \dots + 100!$ is divided by $2$.
   1. 1 answer
   2. asked by Lily
   3. 148 views
6. Find the largest positive integer $n$ such that\[\frac{(n + 1)^2}{n + 2}\] is an integer.
   1. 1 answer
   2. asked by Lily
   3. 158 views
7. What is the largest integer $n$ such that $11^n$ divides $1,000,000!$ ?
   1. 1 answer
   2. asked by Lily
   3. 160 views
8. The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$What is the smallest positive integer that
   1. 1 answer
   2. asked by Dallas
   3. 162 views
9. Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $11.$ When the number $N$ is expressed in
   1. 1 answer
   2. asked by Lily
   3. 169 views
10. let a be a rational number and b be an irrational number. Which of the following statements are true?A. The sum of a and b is
    1. 1 answer
    2. 191 views
11. A palindrome is a number that is the same when read forwards and backwards, such as $43234$. Find the number of $4$-digit
    1. 1 answer
    2. asked by alice
    3. 206 views
12. How many integers from $1$ to $9$ are divisors of the five-digit number $24,519$?
    1. 1 answer
    2. asked by shelly
    3. 185 views
13. Find all numbers $r$ for which the system of congruences:x == r mod 6 x == 9 mod 20 x == 4 mod 45 has a solution.
    1. 1 answer
    2. asked by Anonymous
    3. 1,477 views
14. For all integers a, b, c, d, determine whether each of the following is TRUE or FALSE, Justify your answer:a)If a|c and b|c,
    1. 2 answers
    2. asked by Steffen
    3. 542 views
15. Find the largest three-digit number that can be written in the form $3^m + 2^n$, where $m$ and $n$ are positive integers.
    1. 1 answer
    2. asked by Mr. Alexander
    3. 852 views
16. Find a positive integer m such that1 2m is a perfect square and 1 3m is a perfect cube. Can you find a positive integer n for
    1. 1 answer
    2. asked by groove
    3. 898 views
17. A positive integer n is such that numbers 2n+1 and 3n+1 are perfect squares. Prove that n is divisible by 8.thanks
    1. 2 answers
    2. asked by Candice
    3. 1,597 views
18. I'm not sure how to start part(a). I believe part (b) is correct, but just in case I would like to make sure it's correct.(a)
    1. 1 answer
    2. asked by Jane
    3. 674 views