3. Diophantine Equations #

Created Wednesday 29 July 2020

Diohphantine Equations - These are polynomial equations for which integral solutions exist.

We need to study only about linear Diophantine equations.

• 
• Solutions(integral) exist for this if gcd(a,b) is a factor of C.
• We are not going to prove this, but the intuition is easy:
  1. gcd(a,b) is a factor of a, b
  2. gcd(a, b) will divide ax+by
  3. We represent this by c.

e.g has solutions, while has no integral solutions.

• We are studying this in order to apply extended Euclidean algorithm.