Homework Help

Solve the diophantine equation: 15x+64y = 1

user profile pic

svjr | Student, Undergraduate | (Level 2) Honors

Posted November 7, 2011 at 3:30 AM via web

dislike 0 like

Solve the diophantine equation: 15x+64y = 1

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted November 28, 2011 at 2:30 AM (Answer #1)

dislike 0 like

Remember that Diophantine equations accept integer solutions, only.

Write the equation in the slope intercept form.

64y = -15x + 1

Dividingy by 64 both sides => y = -(15/64)*x + 1/64

Notice that the only factor that can divide c (c=1) is 1.

From this point, you have no reason to continue to solve the equation because it will not lead you to integer solutions.

ANSWER: The Diophantine equation has no integer solutions.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes