Get the solution to "Decide whether each of these integers is congruent..."

Mariyah Best

Open question

2022-08-20

Decide whether each of these integers is congruent to 3 modulo 7.
-17

Cristofer Briggs

Beginner2022-08-21Added 8 answers

Definitions
Algorithm for division Let d be a positive integer and let a be an integer.Then there are nique integers q and r with

0 \leq r < d

such that a=dq+r
q is called the quotient and r is called the remainder

q = a \div d

r = a b mod d

Solution

3 b mod 7

Since -17 is smaller than 3, we should be able to obtain -17 by consecutively subtracting 7 from 3 if

- 17 \equiv 3 b mod 7

3 b mod 7

\equiv 3 - 7 b mod 7

\equiv - 4 b mod 7

\equiv - 4 - 7 b mod 7

\equiv - 11 b mod 7

\equiv - 11 - 7 b mod 7

\equiv - 18 b mod 7

We then note that 3\bmod 7 is equivalent with -11 and -18.

3 b mod 7

is then not equivalent with -17, since -18 < -17 < -11.
Note:

- 17 b mod 7 \equiv 4 b mod 7

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?