Winter 2012 Kronenthal Math 210 Section 011 Homework 7 Due Date: Thursday Januar

Winter 2012 Kronenthal Math 210 Section 011 Homework 7 Due Date: Thursday January 26 by 11:00 am A few reminders: Before attempting these graded problems be sure to try the ungraded questions; they might help you with these problems. Your homework must be written neatly explained completely and stapled if you turn in more than one piece of paper. Problems must be presented in order. Work not satisfying these criteria will be penalized. You are welcome to discuss the mathematics behind the homework with others but you must write the answer to each problem by yourself. 1.
Winter 2012 Kronenthal Math 210 Section 011 Homework 7 Due Date: Thursday January 26 by 11:00 am A few reminders: Before attempting these graded problems be sure to try the ungraded questions; they might help you with these problems. Your homework must be written neatly explained completely and stapled if you turn in more than one piece of paper. Problems must be presented in order. Work not satisfying these criteria will be penalized. You are welcome to discuss the mathematics behind the homework with others but you must write the answer to each problem by yourself. 1. Find ALL solutions x 2 Z to the congruence 259x 26 (mod 2012). 2. Use induction to prove that for any n 2 NXn i=1 3i = 3n+1 ?? 3 2 3. A sequence is a list of objects such as numbers. We will dene a sequence of integers in the following way. The rst term denoted S1 will be 1. The second term denoted S2 will be 2. For all integers m 3 the mth term of the sequence will be found by the formula Sm = Sm??1 + 6Sm??2. (In other words to nd the mth term of the sequence add the previous term to 6 times the term before that.) Use induction to prove that for all n 2 N Sn

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