M135F08A5 - MATH 135 Fall 2008 Assignment #5 Due: Thursday...

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Unformatted text preview: MATH 135 Fall 2008 Assignment #5 Due: Thursday 23 October 2008, 8:20 a.m. Hand-In Problems 1. In each part, state the answer. No justification is necessary. (a) Does the linear Diophantine equation 15 x + 39 y = 28 have any solutions? (b) Does the linear Diophantine equation- 148 x- 370 y = 111 have any solutions? (c) Determine the complete solution to 1980 x- 1923 y = 9. (d) Determine the prime factorization of 22 680. (e) Determine the prime factorization of 66 150. (f) Determine gcd(22 680 , 66 150). (g) Determine the number of positive divisors of 22 680. (h) A positive divisor of 22 680 is chosen at random. What is the probability that this divisor is even? 2. Determine all non-negative integer solutions to the linear Diophantine equation 176 x + 256 y = 5200. 3. The complete solution to the linear Diophantine equation 1911 x + 741 y = 273 is x = 49 + 19 n y =- 126- 49 n n Z . (You do not need to show this.) Determine all non-negative solutions to the linear Diophantine equation 1911...
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This note was uploaded on 09/04/2009 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.

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M135F08A5 - MATH 135 Fall 2008 Assignment #5 Due: Thursday...

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