Evaluating the congruence $(1+195) \pmod 7$

Question

$$(1 + 195) \pmod 7 \equiv \quad ?$$

How would I get the answer? Because when I divide $196 / 7$ I get $28$ which is not a decimal to multiply by $7$.

You seem to be using a strange way of working things out mod $n$ in some of your questions. Do you know what modular arithmetic is? When reducing mod $n$ you are really looking for the remainder upon division by $n$. — fretty, May 29 '13 at 18:01
@MethodManX For future questions, please try to come up with a more informative title. "Answer to this question" fits, or should fit, every question on Mathematics.SE. If you don't succeed in this, please indicate this in your question body (e.g. at the end), so that people may feel more at liberty to change the title. — Lord_Farin, May 29 '13 at 18:07

score 2 · Answer 1 · answered May 29 '13 at 18:01

2

$196$ is divisible by $7$, so $196 \equiv 0 \mod 7$

answered May 29 '13 at 18:01

Mark Bennet

score 0 · Answer 2 · answered May 29 '13 at 18:01

0

195 mod 7 is 6, and 1 mod 7 is 1

which means the sum is 7 mod 7 = 0

you recieve 28 which is 0 mod 7, which is the answer

answered May 29 '13 at 18:01

DanielY

2 Answers2