Suppose c is any integer. If c mod 15 = 3, whatis 10c mod 15? In other words, if division of c by15 gives a remainder of 3, what is the remainderwhen 10c is divided by 15? Your solution shouldshow that you obtain the same answer no matterwhat integer you start with.

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Answered: Suppose c is any integer. If c mod 15 =…

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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On National Public Radio, the "Weekend Edition" program on Sunday, July 29, 2001, posed the following puzzle: Draw a three-by-three square three boxes across by three boxes down. Put the fraction 3/8 in the first square in the first row. Put the fraction 1/4 in the last square in the second row. The object is to put a fraction in each of the remaining boxes, so the three numbers in each row, each column, and each of the long diagonals add up to I. Solve this puzzle by letting seven variables represent the seven unknown fractions, writing eight equations for the eight sums, and solving by the Gauss-Jordan method.
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 can be proved to be true for n=k+1. Explain why this does not prove that the statement is true for all positive integers. Is the statement true for all positive integers? Why?

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Suppose c is any integer. If c mod 15 = 3, what is 10c mod 15? In other words, if division of c by 15 gives a remainder of 3, what is the remainder when 10c is divided by 15? Your solution should show that you obtain the same answer no matter what integer you start with.