Unformatted text preview: integers greater than 1. 7. Use the Euclidean and extended Euclidean algorithms to ﬁnd the gcd of the following pairs of numbers and to represent the gcd as a linear combination of the input data: a) (45 , 75), b) (666 , 1414), c) (102 , 222) d) (20785 , 44350). 8. Let m, n be positive integers and let a be an integer greater than 1. Show that ( a m1 , a n1) = a ( m,n )1. 9. Show that every positive integer can be written as the product of possibly a square and a squarefree integer. Recall a square free integer is an integer that is not divisible by any perfect square other than 1. 1...
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 Fall '07
 Santos
 Number Theory, Integers, Prime number, Euclidean algorithm, Qn, relatively prime integers, square free integer, biggest prime factor

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