Question

What is the minimum value of abs(779-1045n-640) as m,n take all integer value? find x if x?

Answer 1

your question should be What is the minimum value of x = abs(779m-1045n-640) as m,n take all integer value? find x if x?

we have to find out minimum value of abs(779m - 1045n - 640) , where abs(x) means absolute value of x .

Let x = |779m - 1045n - 640|
x = |19 × 41m - 19 × 55n - 640|
x = |19 × 41m - 19 × 55n | - 640
x = 19|41m - 55n| - 640
Let |41m - 55n| = r , where r is positive integers
then, x = 19r - 640 ≥ 0
only when r = 34
then, x = 19 × 34 - 640 = 646 - 640 = 6

hence, minimum value of x = 6