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Quiz-Linear Diophantine Equation


(1) When Mr. Smith cached a check at his bank, the teller mistook the number of cents for the number of dollars and vice versa. Unaware of this, Mr. Smith spent 68 cents and then noticed to his surprise that he had twice the amount of the original check. Determine the smallest value for which the check could have been written.

(2) Divide 100 into two summands such that one is divisible by 7 and the other by 11.
(hint: 7x +11y = 100)

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DIOPHANTINE HISTORY


Long time ago....
A Greek mathematician Diophantus .Save that he lived in Alexandria sometime around 250 AD.Eventhough his work were written in Greek and he diplayed the Greek genius for theoretical abstraction,he was most likely a Hellenized Babylonion.

This is my fav:
Lies on his stone is a wording of an epigram-problem about his career life;
His boyhood lasted 1/6 of his life,his beard grew after 1/12 more,after 1/7 more he married, and his son was born 5 years later,the son life to half his age and the father died 4 years after his son.Assume x was the age at which Diophantus died,so
(1/6)x + (1/12)x + (1/7)x + 5 + (1/2)x + 4 = x
with solution x=84.This puzzle implies that Diophantus lived to be about 84 years old. However,in what year or even in what century is not certain.


Arithmetica
The Arithmetica is the major work of Diophantus and the most prominent work on algebra in Greek mathematics. It is a collection of problems giving numerical solutions of both determinate and indeterminate equation. Of the original thirteen books of which Arithmetica consisted only six have survived, though there are some who believe that four Arab books discovered in 1968 are also by Diophantus. Some Diophantine problems from Arithmetica have been found in Arabic sources.During the Dark Ages, Diophantus was forgotten and like many other mathematical treatises from the classical period, Arithmetica survived through the Arab tradition.



More to know:
1. http://en.wikipedia.org/wiki/Diophantus

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