102 Find x y Z satisfying the equation of By B ezouts Lemma

10.2 Find x, y Z satisfying the equation of By B ezout’s Lemma, the equation 11x + 13y = 1 has at least one solution x,y Z.

Solution

13*5=65=66-1=11*6-1

So,

11*6-13*5=1

So, x=6,y=-5 is one such solution

General solution would be

x=6+13n, y=-5-11n , n is any integer