Difference between revisions of "MA 453 Spring 2009 Walther Homework" - Rhea

Revision as of 11:27, 22 January 2009

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 [[Category:MA453Spring2009Walther]]
-Chapter 0: 24, 25, 7, 14, 19, 21
-Due Thursday, January 22
--- It's kind of funny that it starts at chapter 0.  Very CS of Joe!  [[User:eraymond|eraymond]] 13:56, 19 January 2009 (UTC)
-[[Problem 24]]
-*If p is prime and p divides a_1a_2...a_n, prove that p divides a_i for some i
-*In class we proved this for the case where <math>p|ab</math>. I was unable to extend that proof for <math>n</math> factors of <math>a</math>. Anyone figure this out?
-**I updated the page with a [[Problem 24|link]] to the solution. -Nick
-Problem 25
-*Use the Generalized Euclid's Lemma to establish the uniqueness portion of the Fundamental Theorem of Arithmetic
-Problem 7
-*Show that if a and b are positive integers, then ab = lcm(a, b) * gcd (a,b)
-*I completed this problem by writing a and b as prime factorizations, with the gcd and lcm having the min and max of their exponents respectively. --[[User:Podarcze|Podarcze]] 15:15, 20 January 2009 (UTC)
-Problem 14
-*Show that 5n + 3  and 7n + 4 are relatively prime for all n
-*You can use Euclid's Algorithm to show that <math>gcd(5n+3,7n+4)=1</math>. Start with <math>(7n+4)=1*(5n+3)+(2n+1)</math> and iterate until the remainder is 0.
-Problem 19
-*Prove that there are infinitely many primes. (hint: use ex. 18)
-[[Problem 21]]
-*For every positive integer n, prove that a set with exactly n elements has exactly 2^n subsets (counting the empty set and the entire set)
---[[User:Aifrank|Aifrank]] 13:56, 18 January 2009 (UTC)

Difference between revisions of "MA 453 Spring 2009 Walther Homework" - Rhea

Revision as of 11:27, 22 January 2009

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