Discrete Structures2080.15 marksNumerical: congruence modulo checkIntegers and Division
What is congruent modulo? Determine whether 37 is congruent to 3 modulo 7 and whether -29 is congruent to 5 modulo 17.
What is congruent modulo? Determine whether 37 is congruent to 3 modulo 7 and whether -29 is congruent to 5 modulo 17. [5]
- Check 1: Is $37 \equiv 3 \pmod{7}$? - Check 2: Is $-29 \equiv 5 \pmod{17}$? If $a$ and $b$ are integers and $m$ is a positive integer, then $a$ is congruent to $b$ modulo $m$ if $m$ divides $(a - b)$. Notation: $$a \equiv b \pmod{m}$$ If they are not congruent, we write