Question 1:For the given pair (x, y) of positive integers, such that 4x-17y=1 and x<1000 how many integer values of y satisfy the given conditions?[1] 56[2] 57[3] 58[4] 59

To solve this problem, we need to find the values of y that satisfy the equation 4x - 17y = 1, given that x is a positive integer less than 1000.

Step 1: Rearrange the equation to solve for y.

4x - 1 = 17y

Step 2: Divide both sides by 17 to isolate y.

y = (4x - 1) / 17

Step 3: Now, we need to find the values of x that make y an integer. Since x is a positive integer less than 1000, we can simply plug in values for x and see which ones work.

Step 4: We start with x = 1 and increase by 1 each time, checking if y is an integer. We stop when x = 1000.

Step 5: Count the number of integer values of y that we found.

After performing these steps, we find that the number of integer values of y that satisfy the given conditions is 59. So, the answer is [4] 59.