Suppose that a and b are integers, a $\equiv$ 11 (mod 19) and b $\equiv$ 3 (mod 19). Find the integer c such that c $\equiv$ a - b (mod 19).

Question

With $0 \le c \le 18$.

I can recall the basic modulo arithmetic properties, but I can't see how to apply them. Any help would be appreciated.

Where is this question from? What have you tried so far yourself? — Mike, Mar 09 '24 at 00:59
See the Congruence Sum, Product, and Polynomial Rules in the linked dupe. — Bill Dubuque, Mar 09 '24 at 01:26

score 1 · Answer 1 · answered Mar 09 '24 at 00:49

1

$$a\equiv11\bmod(19)\\b\equiv3\bmod(19)\\\Rightarrow a-b\equiv8\bmod(19)\Rightarrow c\equiv8\bmod(19)$$

So c is any number of the form 19k+8

answered Mar 09 '24 at 00:49

RandomGuy

Please strive not to post more (dupe) answers to dupes of FAQs. This is enforced site policy, see here. It's best for site health to delete this answer (which also minimizes community time wasted on dupe processing.) – Bill Dubuque Mar 09 '24 at 01:27

1 Answers1