4383_Notes_2o5 - Number Theory Section 2.5 Linear...

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Section 2.5 Linear Diophantine Equations A Diophantine equation is an equation in one or more unknowns that is to be solved in the integers. The name honors the mathematician Diophantus, who may have lived in the 3 rd century AD in Alexandria. Diophantus’ great work Arithmetica may be considered an early treatise on algebra because it was one of the earliest books to contain symbols for the unknown and arithmetic operations. Here is the classic problem about Diophantus: 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 lived to half of his father’s age and the father died 4 years after the son. Typical Diophantine equations that are of interest are polynomials in two or more variables that are solved in the integers. One such equation you should all be familiar with is 2 2 2 + = a b c , find integers that satisfy the Pythagorean theorem. Another Diophantine equation :
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This note was uploaded on 02/21/2012 for the course MATH 4383 taught by Professor Flagg during the Spring '09 term at University of Houston.

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4383_Notes_2o5 - Number Theory Section 2.5 Linear...

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