### 1.

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

### 2.

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

### 3.

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

### 4.

Explain the use of the term “induction hypothesis.”

### 5.

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