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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
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