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  Pick.
A) 59
B) 57
C) 55
D) 58
E) 60

Rationale: "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 + 17 n 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 + 17 n ≤ 1000 17 n ≤ 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 . answer : a"
Answer: A