Question

write a formula which describes all fractions which kiss 7/11

Number Theory

Answer 1

solution:

To solve this Diophantine equation, we use the Euclidean algorithm.

7x - 11y = 1 or -1

First lets check for 1 :
7x - 11y = 1

Clearly x= 8 and y = 5
So, 5/8 kisses it

Now check for -1 :
7x - 11y = -1

x = 3 and y = 2 works

So, for -1, fraction 2/3 kisses it

So, for 7/11, we have 5/8 and 2/3