direct method-Math

Prove or disprove the following: If the integer n is divisible by 3 then n^2 is divisible by 3. Use the direct method of proof as outlined in the notes.

  1. 👍
  2. 👎
  3. 👁
  1. If n is divisible by 3, it can be written 3a, where a is an integer.

    n^2 = 9 a^2, where a^2 is also an integer, is also divisible by three, since 9 = 3 x 3.

    I don't have your notes so have no idea what kind of proof they expect.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Determine the largest possible integer n such that 942! is divisible by 15n.

  2. arithmetic

    Prove that the product of three consecutive even numbers is divisible by 48

  3. math

    A number is chosen from the first 24 positive integers. Find the probability that: a) the number is divisible by 3 given that it is divisible by 4 b) the number is divisible by 6 given that it is divisible by 3 Just need help with

  4. Math

    Prove that 7^7-7^6 is divisible by 6

  1. Algebra 2

    The smallest integer that can be added to -2m^3 − m + m^2 + 1 to make it completely divisible by m + 1 is:

  2. Math

    Prove that 1 * 3 * 5 * ... * 2345 + 2 *4 * 6* ... * 3456 is divisible by 6789.

  3. Algebra 1 Polynomials

    Suppose n is an integer. Select all statements below that are true: (choose 3) A) n^2 + n is always an even integer*** B) n^2 + n is always an even integer when n is even*** C) n^2 + n is always an even integer when n is odd*** D)

  4. Precalculus with Trigonometry

    Prove or disprove the following identity: cos (x+pi/6) +sin (x-pi/3) = 0

  1. Math

    True or fals: a number is divisible by 8 if it is divisble by 4 and divisible by 2? And how many variations of 3_2_ are divisible by six?

  2. Math

    Prove that a^3 ≡ a (mod 3) for every positive integer a. What I did: Assume a^3 ≡ a (mod 3) is true for every positive integer a. Then 3a^3 ≡ 3a (mod 3). (3a^3 - 3a)/3 = k, where k is an integer a^3 - a = k Therefore, a^3

  3. maths-

    if n is an odd positive integer, then prove that n^2 -1 is divisible by 8

  4. Mathematics

    Can anyone check my answers please True or false 927 is divisible by 3 and 9 true 13,012 is divisible by 9 false 7,434 is divisible by 6 true 2,064 is divisible by 2,4,and8 true 96,240 is divisible by 2,3,5, and 10 true Am I

You can view more similar questions or ask a new question.