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

Mariyah Best

Mariyah Best

Open question

2022-08-20

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

Answer & Explanation

Cristofer Briggs

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 0r<d such that a=dq+r
q is called the quotient and r is called the remainder
q=a ÷ d
r=abmodd
Solution
3bmod7
Since -17 is smaller than 3, we should be able to obtain -17 by consecutively subtracting 7 from 3 if 173bmod7.
3bmod7
37bmod7
4bmod7
47bmod7
11bmod7
117bmod7
18bmod7
We then note that 3\bmod 7 is equivalent with -11 and -18. 3bmod7 is then not equivalent with -17, since -18 < -17 < -11.
Note: 17bmod74bmod7

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