Abstract Algebra: Theory and Applications

Use Sage to express $123456792$ as a product of prime numbers.

Find the greatest common divisor of $84$ and $52\text{.}$

Find integers $r$ and $s$ so that $r(84)+s(52)=gcd(84,52)\text{.}$

Explain the use of the term “induction hypothesis.”

What is Goldbach’s Conjecture? And why is it called a “conjecture”?