I know the rule to check divisibility by 9: check if the sum of the digits of the number is divisible by 9. But what if the number is negative?
Thanks in advance!
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4It's the same. Multiplying by $-1$ doesn't change whether a number is divisible by $9$. – Qiaochu Yuan May 19 '15 at 00:50
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Cool! Thanks!!! – matheuscscp May 19 '15 at 00:51
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Multiplying by -1 doesn't change anything. If we have 18, which we know is divisible by 9, we just multiply it by -1 to get -18 and then we do the same to how many times 9 goes into 18 to get -2, and see that 9 goes into -18 -2 times, -2 is an integer so the rule holds up.
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actually, multiplying by -1 doesn't change anything in any divisibility test, right? if I only wanna know if a number is divisible by another... the sign would matter if I wanted to know the exact remainder, right? like -10 mod 7, which is 4 (different from 10 mod 7, which is 3) – matheuscscp May 19 '15 at 03:41
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Correct, it does not change anything in any divisibility test, but it does when dealing with modulo. – May 19 '15 at 21:19
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As @user1693330 stated, the divisibility rule does not change. You can also look at it like this:
The divisibility rule is "check if the sum of the digits of the number is divisible by 9", but "-" isn't a digit.
It is the same as other divisibilities.
