Problem 2RQ

a) Define what it means for a and b to be congruent modulo 7.

b) Which pairs of the integers –11, –8, –7, –1.0, 3, and 17 are congruent modulo 7?

c) Show that if a and b are congruent modulo 7, then 10a + 13 and –4b + 20 are also congruent modulo 7.

Solution:

Step 1

In this problem we need to define the meaning of a and b to be congruent modulo 7. Then we need to find the pairs which are congruent to modulo m for the integers –11, –8, –7, –1.0, 3, and 17 and finally we also need to show that and are congruent modulo 7 if a and b are congruent modulo 7.