## The integer 17 belongs to the residue class modulo m of 24. Find m.

(Old) Question posted by Felipe Maia to math.stackexchange.com :

The integer 17 belongs to the residue class modulo m of 24. Find m.

(…) I thought of calculating m for the values ​​of the divisors of 24, that is, making m belonging to D (24). (…)

Definition of residue. The number $r$ in the congruence $a\equiv r\pmod m$ is called the residue of $a\pmod m$. In the case at hand $r=17$ and $a=24$.

This means that for some integer $k$ the following equality holds $24=17+km$. You should then have $km=7$, where $k$ and $m$ are positive integers. This implies that $m=7$, because $7$ is a prime number, that is, it has no divisors, except $1$ and $7$.

## Sobre Américo Tavares

eng. electrotécnico reformado / retired electrical engineer
Esta entrada foi publicada em Math, Mathematics Stack Exchange, Number Theory com as etiquetas , , , , , . ligação permanente.

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