Diophantine Equations

One Variable

Diophantine Equations are equations where we look for integer solutions only. Watch the following video on one-variable Diophantine Equations:

Multiple Variables

Diophantine equations are important, since we need to consider one for a specific theorem.

If $a$ and $b$ are integers, then

$ax + by = GCD(a, b)$

Has integer solutions for $x$ and $y$

We'll cover how to solve this problem in the next module, but for now, try to think about it yourself.

Think about it: How might you solve for integer x and y? Hint: The quotient-remainder theorem can be very helpful here.