Discrete Math: Number Theory and Modular Arithmetic

Find the GCD of 1005, 105 using the Euclidean algorithm.

Using Euclid’s Algorithm, find the GCD of 480 and 156.

Prove that if $x$ is odd, then $x^2$ is odd.

Prove that if $x$ and $y$ are odd, then $xy$ is odd.

Prove: If $n$ is an odd integer, then $n^2$ is odd.

Prove: The sum of two even integers is even.

What is 53 equivalent to mod 3?

Find the prime factorization of 24.

Find the prime factorization of 75.

Find the prime factorization of 84.

What is the prime factorization of 50?

Write the prime factorization of 120.

Write the prime factorization of 280.

Write the prime factorization of 540 using the factor tree method.

Find the prime factorization of 10,800.

Show that $\sqrt{2}$ is irrational.

If $3|a^2$ then $3|a$ for any integer $a$.

Solve the linear congruence: $5x \equiv 2 \pmod{9}$.

Solve $17x \equiv 3 \pmod{29}$ using Euclid's Algorithm.

Prove that every integer greater than 1 can be written as the product of primes.