Determine which positive inlegers are of the form 999x + 1001y, where x and y are nonnegative integers. Confirm that your results agree with the Exercises 1–3.
Exercise 1
Show that whenever n ≥ (a − 1)(b −1), there is a nonnegative solution of ax + by = n.
Exercise 2
Show that if n = ab − a − b, then there are no nonnegative solutions of ax +by = n.
Exercise 3
Show that there are exactly (a −1)(b − 1)/2 nonnegative integers n < ab −a − b such that the equation has a nonnegative solution.
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