Ask Question
14 November, 16:40

Assume a and b are both integers and a > 0. Define a remainder after the division of b by a to be a value r such that r ⥠0, r < a, and there exists an integer q for which b = aq + r. a) Prove uniqueness. That is, if r1 and r2 are both remainders after the division of b by a, then r1 = r2. Y

+3
Answers (1)
  1. 14 November, 18:37
    0
    r1=r2

    Step-by-step explanation:

    Initially, let's assume there are two remainders r1, and r2. This must fit the following equations:

    b=a. q + r1 (equation 1)

    b=a. q + r2 (equation 2)

    Because we have the same variable b in both equations, we can make equal both expressions, and solving:

    a. q + r1 = a. q + r2

    - r2 = - r2

    a. q + r1 - r2 = a. q + 0

    a. q + r1 - r2 = a. q

    -a. q = - a. q

    0 + r1 - r2 = 0

    r1 - r2 = 0

    +r2 = r2

    r1 + 0 = r2

    r1 = r2 And this is what we want to proof.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Assume a and b are both integers and a > 0. Define a remainder after the division of b by a to be a value r such that r ⥠0, r < a, and ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers