Answer:
-1011
Step-by-step explanation:
An integer that is congruent to 1 mod{23} is of the form 23n+1.
Therefore, we form the inequality 23n+1<-999, and find the largest possible integer n. We get
23n+1<-999
23n<-1000
n < 1000/23, or n < -43.48
The largest possible negative integer n is -44. We plug it in for n to get 23 x -44 +1 =-1011.
