Find the least residue

Question

for $125$ mod $13$ and $-43$ mod $7$

$13$ goes into $125$ $9$ times with a remainder of $8$

$7$ goes into $-43$ $6$ times with a remainder of $1$

So the least residues are $8$ and $1$(possibly $-1$)? Is it really that easy?

You seem to have ignored the minus sign in $-43$. The remainder is always some $r$ with $0\leqslant r < d$, where $d$ is the divisor. — Fimpellizzeri, Jan 24 '20 at 14:51

score 1 · Accepted Answer · answered Jan 24 '20 at 14:52

1

$-43=-7\times7+6,$ so $-43\bmod 7=6.$

answered Jan 24 '20 at 14:52

J. W. Tanner

Can you explain why? – K. Gibson Jan 24 '20 at 14:55
1

Because the remainder $r$ satisfies $0\leqslant r < d$, where $d$ is the divisor. – Fimpellizzeri Jan 24 '20 at 14:56

1 Answers1