Is there an integer solution of 34x17y1SolutionSOLUTION The

Is there an integer solution of 34x+17y=1?

Solution

SOLUTION:

The equation of the form : ax+by=c, a,b,c are integer is called a Diophentine equation.

This Diophentine equation will have a solution if and only if gcd(a,b) divides c.

Here the equation is 34x+17y=1.

gcd(34,17)=17.

Since 17 does not divide 1, so the equation has no integer solution.