Question

Find all the numbers of the form 517xy that are divisible by 89.

Answer 1

517xy is the number. The smallest number is 51700. Dividing 51700 by 89, gives the remainder as 80. That is
51700 = 89 $\times$ 580 + 80.
89 $\times$ 580 = 51620.
Hence the next numbers are 51709, and 51798. Then the numbers goes above 51800.
Thus there are two number of the form 517xy, and the numbers are 51709 and 51798.