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MCII-B Number Theory 4.26

 
 
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Re: MCII-B Number Theory 4.26
LensmireJohn - 2024年08月21日 Wednesday 08:37
 

For (mod 11), I would recommend getting use to alternating + and - from right to left. We're really using the rule proved in 4.25b (which helps understand why it's right to left).

I'd like to let you figure out the problem (and it's a bad example for explaining the rule because of the repeated digits), so let's look at a few other examples:

  • $1234 \equiv +4-3+2-1 = 2 \pmod{11}$
  • $9753 \equiv +3-5+7-9 = -4 \equiv 7 \pmod{11}$
  • $97531 \equiv +1-3+5-7+9 = 5 \pmod{11}$

Hope this helps.