Question

List all integers between −100 and 100 that are congruent to −1 modulo 25.

Answer 1

"-1 modulo 25" is "1 less than a precise multiple of 25". 
So what are the exact or precise multiples of 25 in the appropriate interval? 
It is -75, -50, -25, 0, 25, 50, 75, and 100. 
Now just subtract 1 from each of them.

So the answers are -76, -51, -26, -1, 24, 49, 74, and 99.