Discrete Mathematics I MATH/CSCI 2112 Fall 2011 Assignment 3 Due Wednesday 14 Oct (1) Prove that 3p2 is irrational. (2) Prove that the sum of two odd primes is never prime. Is the statement true if the word odd is deleted? (3) Given k 2 N an m 2 N is a perfect kth power if m = nk; 9n 2 Z (a) How are perfect kth powers recognizable from their prime factorizations? (b) Show that if an n 2 Z is perfect square and a perfect cube it is lo a perfect sixth power. (4) Prove that 8n 2 N (3n)! 3n 2 N (5) For natural numbers m; n 2 N show lcm(m; n) gcd(m; n) = mn (lcm is least common multiple; gcd is greatest common divisor.) 1
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