Greatest Common Divisor / Lowest Common Multiple: Level 4 Challenges Practice Problems Online

For $m>1$ , it can be proven that the integer sequence $f_m(n) = \gcd(n+m,mn+1)$ has a fundamental period $T_m.$ In other words, $\forall n \in \mathbb{N}, \space f_m(n+T_m) = f_m(n).$ Find an expression for $T_m$ in terms of $m,$ and then give your answer as $T_{12}.$

When 2017 is divided by a 2-digit number, what is the largest possible remainder?

Bonus: Generalize this problem.

Find the largest integer $n$ such that $n$ is divisible by all positive integers less than $\sqrt[3]{n}$ .

Find the sum of all integers $k$ with $1\leq k\leq 2015$ and $\gcd(k,2015)=1$ .

What is the greatest common factor of all integers of the form $p^4 - 1$ where $p$ is a prime number greater than 5?

Intro

Concept Quizzes

Challenge Quizzes

Greatest Common Divisor / Lowest Common Multiple: Level 4 Challenges

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.