Question

Discrete Math, Modulo explanation

12 ≡ -23(mod7)
I know I am supposed to take
12-(-23) = 35 and
35 mod 7 is 5

but why? more to my question will be inside

Answer 1

to me this question is asking

is 12 congruent to -23mod 7 which would be (-23/7) remainder which is essentially -2

Answer 2

sorry 35 mod 7 would be 0

Answer 3

\(a\cong b \mod n \iff \dfrac{a-b}{n}\in \mathbb{Z} \)

Answer 4

i.e. a is congruent to b mod n if and only if n divides a-b

Answer 5

i.e. you have 0 remainder

Answer 6

Thank you