Question 1

# The number of positive integer valued pairs (x, y), satisfying 4x - 17 y = 1 and x < 1000 is:

Solution

y = $$\frac{4x-1}{17}$$

The integral values of x for which y is an integer are 13, 30, 47,......

The values are in the form 17n + 13, where $$n \geq 0$$

17n + 13 < 1000

=> 17n < 987

=> n < 58.05

=> n can take values from 0 to 58 => Number of values = 59