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(Euclid) Prove that there areinfinitely many primes. [ Use proof by contradiction (Appendix A).Assume there are only finitely many primes p1 , p2 , . . . , pk, and reach acontradiction by showing that the number p1p2 ? ? ?pk `1 is not divisible by anyof p1,p2,...,pk.]

Show transcribed image text (Euclid) Prove that there are infinitely many primes. [ Use proof by contradiction (Appendix A). Assume there are only finitely many primes p1 , p2 , . . . , pk , and reach a contradiction by showing that the number p1p2 ? ? ?pk '1 is not divisible by any of p1,p2,...,pk.]

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Jean KeelingLv2

19 Mar 2019

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Problem: Divisibility and Divisibility Rules There are many rules to determine if a number is divisible by other smaller numbers. In basic arithmetic courses, you learned divisibility and discussed a few common divisibility rules. Your task is to determine if the given number is divisible by 9 but is not divisible by 11 Given number: 7,176,825,942,116,027,211 Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your calculator 1. Research the topic of divisibility 2. Research the divisibility rules for 9 and 11. 3. Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11. "Note:I am telling you that the number IS divisible by 9 and IS NOT divisible by 11. Do not try to show the opposite of this statement. 4. Include the following information in a report, in this order: a. Explain (in a few sentences) the topic of divisibility, including any correct terms that apply b. Explain in your own words the divisibility rule of 9. C. Give an example using another number to help the explanation. d. Show how the given number is divisible by 9. Work out all your steps. e. Explain in your own words the divisibility rule of 11 f. Give an example using another number to help the explanation. g. Show how the given number is not divisible by 11. Work out all your steps. 5. You must locate a minimum of 2 sources to help you complete this project. More than two sources, though not required, can be used if it helps to give detail to the project. a. You must use at least one book or E-book (other than your textbook). Do not use the dictionary for your definition. b. You must use at least one website. Do not use Wikipedia c. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the problem. Your sources should be relevant to the project and not just be a math source because it has math in the context d. 6. Correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, you can try using the website EasyBih Be sure to do the entire project typed neatly 7. Papers will be compared for similarity Plagiarism is against the academic honesty policy and will receive a zera. Note: A detailed Grading Rubric is provided on Canvas and on the assignment submission link The due date for the project is listed on Canvas. The Math/Analytical Project must be submitted through Canvas. Directions for submitting can be found in the Course Syllabus and on Canvas.

Show transcribed image text Problem: Divisibility and Divisibility Rules There are many rules to determine if a number is divisible by other smaller numbers. In basic arithmetic courses, you learned divisibility and discussed a few common divisibility rules. Your task is to determine if the given number is divisible by 9 but is not divisible by 11 Given number: 7,176,825,942,116,027,211 Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your calculator 1. Research the topic of divisibility 2. Research the divisibility rules for 9 and 11. 3. Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11. "Note:I am telling you that the number IS divisible by 9 and IS NOT divisible by 11. Do not try to show the opposite of this statement. 4. Include the following information in a report, in this order: a. Explain (in a few sentences) the topic of divisibility, including any correct terms that apply b. Explain in your own words the divisibility rule of 9. C. Give an example using another number to help the explanation. d. Show how the given number is divisible by 9. Work out all your steps. e. Explain in your own words the divisibility rule of 11 f. Give an example using another number to help the explanation. g. Show how the given number is not divisible by 11. Work out all your steps. 5. You must locate a minimum of 2 sources to help you complete this project. More than two sources, though not required, can be used if it helps to give detail to the project. a. You must use at least one book or E-book (other than your textbook). Do not use the dictionary for your definition. b. You must use at least one website. Do not use Wikipedia c. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the problem. Your sources should be relevant to the project and not just be a math source because it has math in the context d. 6. Correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, you can try using the website EasyBih Be sure to do the entire project typed neatly 7. Papers will be compared for similarity Plagiarism is against the academic honesty policy and will receive a zera. Note: A detailed Grading Rubric is provided on Canvas and on the assignment submission link The due date for the project is listed on Canvas. The Math/Analytical Project must be submitted through Canvas. Directions for submitting can be found in the Course Syllabus and on Canvas.

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