# Find the integer a such that a) a\equiv43 and (mod

Find the integer a such that a) $a\equiv 43$ and (mod 23) and $-22\le a\le 0$.
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kalupunangh
Solution:
a) $a\equiv 43$ (mod23)
We can find a such that $-22\le a\le 0$ by consecutively subtracting 23 from 43 until we obtain a value between -22 and 0.
$a\equiv 43$ (mod 23)
$\equiv 43-23$ (mod 23)
$\equiv 20$ (mod 23)
$\equiv 20-23$ (mod 23)
$\equiv -3$ (mod 23)
Since -3 is between -22 and 0:
$a=-3$