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GingerAle

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 #11
avatar+2511 
+1

Wow! We are having a meltdown, aren’t we? What happened? Did you lose your canteen privileges?

 

My answer is the same as Sir Alan’s?  Did you use a computer to analyze this or did you do it the old-fashioned way?  Never mind, I already know the answer.  Of course, my answer is the same as Sir Alan’s, because brilliant minds think alike. Our answers are both correct, so they have to be the same.

 

 Why do you think this is plagiarism?  In this post:  http://web2.0calc.com/questions/big-cheese#r4  I used an analogy of embezzlement to explain plagiarism to you.  This was reasonable because you were a banker, and you’re probably in the “Big House” for this very reason, so, it seemed like you would understand this.  In that post, I said, “It’s always a good idea to make sure the answer you are copying is the correct answer, because you are less likely to get caught (most of us learn that in grade school). . .”

 

See, Sir Alan’s answer was correct and mine was not, so that kind of, sort of contradicts your accusation, unless I purposely did that to throw the bloodhounds off the scent.   Yep, we brilliant, genetically enhanced chimps will do things like that when we have a mind to.  We know how to use our noodles! We also post parallel solutions when a student has a problem understanding a presentation, or just when we blŏŏdy well feel like practicing. 

 

Anyway, I can understand why you think having the same answer as someone else is plagiarism.  You post computer generated answers, usually preceded by blarney of the most useless kind, believing them to be solutions.  The only time you ever post a true solution is when you’ve plagiarized it. It’s the “Thick as Thieves” theory. Thieves (embezzlers) usually believe everyone else is a thief, too.  The same applies to plagiarists.   

 

I am surprised you use the “phony as a $3 bill” cliché.  I would think you being a banker would know $3 notes were issued by several banks in the mid-nineteenth century –there is nothing phony about them.  Of course, you were a little boy then and probably not too bright or aware.

 

Anyway, Mr. Banker, It is a sad thought to be a “has been.” However, I want you to know I do not think of you as a “has been,” nope, not at all.  I think of you as a “never were.”

 

Well, I think I’ll have a snack: a few gingersnaps and some Canada Dry Ginger Ale. You should try it, after your canteen privileges are restored. 

 

Until next time, Mr. Banker, don’t take any wooden nickels. Cheers.

Mar 17, 2017
 #4
avatar+2511 
+9

Solution for (n) (smallest positive integer that satisfies the system of congruencies).

n mod 1103 = 1041

n mod 1303 = 859

n mod 2003 = 1095

 

\(\begin{array}{rcll} n &\equiv& {\color{red}1041} \pmod {{\color{green}1103}} \\ n &\equiv& {\color{red}859} \pmod {{\color{green}1303}} \\n &\equiv& {\color{red}1095} \pmod {{\color{green}2003}} \\ \text{Let } m &=&1103 \cdot 1303\cdot 2003 = 2878729627 \\ \end{array} \)

\(\text {1103, 1303, and 2003 are coprime numbers (they are actually prime).}\\\)

\(\small{ \begin{array}{l} n = {\color{red}1041} \cdot {\color{green}1303\cdot 2003} \cdot \underbrace{ \underbrace{ \underbrace{ \underbrace{ \underbrace{ \underbrace{ [ { (\color{green}1303\cdot 2003)}^{\varphi({\color{green}1103}) -1 } \pmod {{\color{green}1103}} ] }_{=\text{modulo inverse }(1303\cdot 2003) mod 1103 }}_{=(1303\cdot 2003)^{1103-1} \mod {1103}} }_{=(1303\cdot 2003)^{1102} \mod {1103}} }_{=(2609909\pmod{1103})^{1102} \mod {1103}} }_{=(211)^{1102} \mod {1103}} }_{=988} + {\color{red}859} \cdot {\color{green}1103\cdot 2003} \cdot \underbrace{ \underbrace{ \underbrace{ \underbrace{ \underbrace{ \underbrace{ [ { (\color{green}1103\cdot 2003) }^{\varphi({\color{green}1303}) -1} \pmod {{\color{green}1303}} ] }_{=\text{modulo inverse } (1103\cdot 2003) mod 1303 } }_{=(1103\cdot 2003)^{1302-1} \mod {1303}} }_{=(1103\cdot 2003)^{1301} \mod {1303}} }_{=(2209309\pmod{1303})^{1301} \mod {1303}} }_{=(724)^{1301} \mod {1303}} }_{=9} +{\color{red}{1095}} \cdot {\color{green}1103\cdot 1303} \cdot \underbrace{ \underbrace{ \underbrace{ \underbrace{ \underbrace{ \underbrace{ [ { (\color{green}1103\cdot 1303) }^{\varphi({\color{green}2003}) -1 } \pmod {{\color{green}2003}} ] }_{=\text{modulo inverse } (1103\cdot 1303) mod 2003 } }_{=(1103\cdot 1303)^{2002-1} \mod {2003}} }_{=(1103\cdot 1303)^{2001} \mod {2003}} }_{=(1437209\pmod{2003})^{2001} \mod {2003}} }_{=(1058)^{2001} \mod {2003}} }_{=195}\\\\ n = {\color{red}{1041}} \cdot {\color{green}{1303}\cdot 2003} \cdot [988] + {\color{red}859} \cdot {\color{green}1103\cdot 2003} \cdot [9] + {\color{red}1095} \cdot {\color{green}1103\cdot 1303} \cdot [195] \\ n = 2684312285772 + 17080167879 + 306880051725 \\ n = 3008272505376 \\\\ n \pmod {m}\\ = 3008272505376 \pmod {2878729627} \\ = 45161 \\\\ n = 45161 + k\cdot 2878729627 \qquad k \in Z\\\\ \mathbf{n_{min}} \mathbf{=} \mathbf{45161} \end{array}} \)

 

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\(\small \text {Related formulas and principles compliments of Leonhard Euler }\scriptsize \text {(totient function),} \\ \small \text {Euclid of Alexandria }\scriptsize \text {(Extended Euclidean algorithm), and Brilliant Chinese mathematicians “Chinese Remainder Theorem” } \\ \small \text {LaTex layout and coding adapted from Heureak’s mathematical solution and Latex presentation:}\\ \tiny \text {http://web2.0calc.com/questions/find-the-smallest-positive-integer-that-satisfies-the-system-of-congruences }\\ \small \text {Produced by Lancelot Link & Co.}\\ \small \text {Directed by GingerAle}\\ \small \text {Sponsored by Nause Corp pharmaceuticals: Makers of } \\ \scriptsize \text { Quantum Vaccines for spooky dumbness at a distance and related contagious dumbness diseases (rCDDs).}\\ \scriptsize \text{ and}\\ \scriptsize \text{ Master Blarney Filters. Now filters most toxins emitted by blarney bankers and related dumb-dumbs. } \\ \)

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Mar 13, 2017