The number of positive integers valued pairs (x, y) satisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is
Choose the correct choice from the following answers
A) 59	B) 57	C) 55	D) 58	E) 60
We are asked to find integer solutions for x,y.   There is no need to apply Euclidian algorithm here, we can get particular solutions simply by plugging in some values.   As y reaches 3 we get:   y’ = 3 and x’ = 13. We need only to solve for x.   General solution for x will be:   x = x’ + bn = 13 + 17n   Hence lower limit for n is n ≥ 0.   Now we’ll find upper limit using given restriction x ≤ 1000. Plugging in general solution we’ll get:   13 + 17n ≤ 1000   17n ≤ 987   n ≤ 58   And our list of possible values of n has following representation:   0, 1,2, 3, ….. , 58   Total number of elements is 59.   59NSWER:59
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The number of positive integers valued pairs (x, y) satisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is