So I just remembered a question I had a while ago about an explanation of the divisibility by $7$ trick where you double the last digit and subtract it from the rest of the number. I think the explanation was something about $-2$ being the multiplicative of $10$ $\pmod{7}$, and I'm not quite sure what that means. Could someone explain?
2026-04-04 05:14:43.1775279683
Question about divisibility rule by $7$ explanation
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$10a+b \mod 7=0 \iff -10a-b\mod7=0 \iff -20a-2b\mod 7=0 \iff a-2b\mod 7=0$, where the last "iff" comes from the fact that $21a \mod 7=0$.