For each of the statements below, say what method of proof you should use to prove them. Then say how the proof starts and how it ends. Bonus points for filling in the middle. a. There are no integers x and y such that x is a prime greater than 5 and x=6y+3. b. For all integers n, if n is a multiple of 3, then n can be written as the sum of consecutive integers. c. For all integers a and b, if a^2 + b^2 is odd, then a or b is odd.

For each of the statements below, say what method of proof you should use to prove them. Then say how the proof starts and how it ends. Bonus points for filling in the middle. a. There are no integers x and y such that x is a prime greater than 5 and x=6y+3. b. For all integers n, if n is a multiple of 3, then n can be written as the sum of consecutive integers. c. For all integers a and b, if a^2 + b^2 is odd, then a or b is odd.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 50E: Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation...

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