a2fall2009 - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER...

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CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE AND SOFTWARE ENGINEERING COMP232-Section DD MATHEMATICS FOR COMPUTER SCIENCE ASSIGNMENT 2 FALL 2009 1. A perfect number is a positive integer that equals the sum of all of its divisors, except the number itself. Give a proof by contradiction that shows that there does not exist a perfect prime number. 2. Prove that if x 3 is irrational then x is irrational, by proving the contrapositive. 3. Give a proof by cases to show that there are no integer solutions to the equation 2 x 2 +5 y 2 =1 4 . 4. Give a proof by contradiction to show that the cube root of 2 is an irrational number. 5. Give a proof by contradiction to show that if the integers 1, 2, ··· , 99, 100 , are placed randomly around a circle (without repetition), then there must exist three adjacent numbers along the circle whose sum is greater than 152. 6. Let n be an integer. Prove that the following statements are equivalent: (a) n 2 is odd (b) 1 n is even (c) n 3
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This note was uploaded on 11/15/2010 for the course ENCS COMP 232 taught by Professor Ford during the Fall '10 term at Concordia University Irvine.

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a2fall2009 - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER...

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