+0

# Help

+1
195
1
+544

If a is congruent to 62 (mod 99) and b is congruent to 75 (mod 99), then for what integer n in the set {1000, 1001, 1002, 1003...  1098} is it true that a-b is congruent to n (mod 99)?

Jul 12, 2019

$$a - b \equiv n \pmod{99}\\ 62 - 75 \equiv n \pmod{99}\\ n\equiv -13 \pmod{99}\\ n \equiv 86 \pmod{99}\\ n \equiv 990 + 86 \pmod{99}\\ n \equiv 1076\pmod{99}$$