a) Assume a = 62 and b = 75. a - b = -13, which equals 86 (mod 99).
The problem is asking n \(\cong\) 86 (mod 99) for the number \(n\) in the set {1000, 1001....1098}.
We can clearly see that 990 (mod 99) = 0. So 990 + 99 = 1089, which is also divisible by 99. So if n = 1089, then \(n \cong 0 (mod99)\). But we need \(n \cong 86 (mod99)\), so n = 1089 - 13 = 1076. The anwer is \(\boxed{1076}\).
Hope this helps,
- PM
+777 
