Discrete Math

Let a, b, c, and d be integers, and let n be a positive integer. Prove that if a is congruent to c mod n and b is congruent to d mod n, then (a-b) is congruent to (c-d) mod n

  1. 👍 0
  2. 👎 0
  3. 👁 154
  1. Given:
    a≡c mod n
    b≡d mod n
    Prove that (a-c)≡(b-d) mod n.

    Let
    a=kn+r ... k,r ∈ ℤ+
    c=ln+r ... l,r ∈ ℤ+
    Subtract:
    (a-c)=(k-l)n

    Similarly,
    (b-d)=(p-q)n ... p,q ∈ ℤ+

    Therefore
    (a-c)≡(b-d) mod n

    1. 👍 0
    2. 👎 0
    posted by MathMate

Respond to this Question

First Name

Your Response

Similar Questions

  1. discrete math

    1)prove that if x is rational and x not equal to 0, then 1/x is rational. 2) prove that there is a positive integers that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive? For

    asked by thisha on September 28, 2006
  2. Math

    Paulo withdraws the same amount from his bank account each week to pay for lunch. Over the past four weeks, he withdrew one hundred twenty dollars. Which rule best applies to determine the change in his account each week? 1. The

    asked by Bilbo on September 11, 2013
  3. MATH

    Let’s agree to say that a positive integer is prime-like if it is not divisible by 2, 3, or 5. How many prime-like positive integers are there less than 100? less than 1000? A positive integer is very prime-like if it is not

    asked by David on April 2, 2010
  4. math

    Let’s agree to say that a positive integer is prime-like if it is not divisible by 2, 3, or 5. How many prime-like positive integers are there less than 100? less than 1000? A positive integer is very prime-like if it is not

    asked by chicken on April 1, 2010
  5. maths

    the non- decreasing sequence of odd integers {a1, a2, a3, . . .} = {1,3,3,3,5,5,5,5,5,...} each positive odd integer k appears k times. it is a fact that there are integers b, c, and d such that, for all positive integers n, añ =

    asked by fui on November 11, 2016
  6. Maths

    Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx

    asked by Matt on July 15, 2009
  7. math

    Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx

    asked by m on July 19, 2009
  8. MAth

    In a set of five consecutive positive even integers, the ratio of the greatest integer to least integer is 2 is to 1. If these integers are arranged from lowest to highest, which is the middle integer in the list?

    asked by john on April 12, 2017
  9. math, algebra

    2a+2ab+2b I need a lot of help in this one. it says find two consecutive positive integers such that the sum of their square is 85. how would i do this one i have no clue i know what are positive integers.but i don't know how to

    asked by sana on January 26, 2007
  10. MATH

    Find the only positive integer whose cube is the sum of the cubes of three positive integers immediately preceding it. Find this positive integer. Your algebraic work must be detailed enough to show this is the only positive

    asked by Janice - Please Help!!! on June 7, 2011
  11. Math

    Can anyone please explain why the one is not the correct answer? Let P(n,m) be a property about two integers n and m. If we want to disprove the claim that "For every integer n, there exists an integer m such that P(n,m) is true",

    asked by Ashley on October 6, 2019

More Similar Questions