+17 Given $m\geq 2$ denote by $b^{-1}$ the inverse of $b\pmod{m}$. That is, $b^{-1}$ is the residue for which $bb^{-1}\equiv 1\pmod{m}$. Sadie wonders if $(a+b)^{-1}$ is always congruent to $a^{-1}+b^{-1}$ (modulo ). She tries the example $a=2$, $b=3$ and $m=7$. Let be the residue of $(2+3)^{-1}\pmod{7}$, and let $R$ be the residue of $2^{-1}+3^{-1}\pmod{7}$, where $L$ and $R$ are integers from $0$ to $6$ (inclusive). Find $L-R$
We have that 2−1≡4(mod7) and 3−1≡5(mod7), so L≡4+5≡1(mod7). Also, 2+3≡5(mod7), so (2+3)−1≡7−5≡2(mod7), so R≡2+5≡7(mod7). Therefore, L−R=6.
Here is a more detailed explanation of the steps involved:
We find that 2−1≡4(mod7) and 3−1≡5(mod7) using the Euclidean algorithm.
We find that L≡4+5≡1(mod7) by applying the congruence ab≡1(modm) to a=2, b=4, and m=7.
We find that R≡2+5≡7(mod7) by applying the congruence ab≡1(modm) to a=5, b=2, and m=7.
We find that L−R=6 by subtracting R from L.
+2489 For the record: The GingerRoot account is NOT under the control of GingerAle.
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Mr. !!BB! You finally got something right for once! Your imbecillic bullshit notions have finally produced something coherent and correct.
The answer is random bullshit; it has nothing to do with the question.
In any case, post #1 isn’t by any of the BBs.
Mr. BB often answers questions correctly, but his solution methods are nebulous. The BB’s solve problems by intuitive reasoning. The reasoning is un-teachable and useless, because it only applies to the question at hand and not as a general solution method.
GA
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+2489 For the record: The GingerBeer account is NOT under the control of GingerAle.
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Typical GA BS. GA uses guest or fake accounts to vent anger then goes like "For the record its not meeee" like we all know its you LMAO!
GingerBeer 2 hours ago
edited by Guest 2 hours ago
Oppsies .. we made a BIG booboo! Didn’t we... Yes we did!
This was supposed to be a guest post and it was snagged by GingerBeer.
OH Darn it! Darn it to the hot place in the bowls of the Earth! How will I ever explain this?
I can’t, so I’ll just delete it. Too bad that it was in plain view for over two (2) hours.
GA
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Oh dear, here GA goes again…
It’s so obvious what is going on.
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