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 ≡ a (mod 3).

Is this a valid method for proving?

  1. 👍
  2. 👎
  3. 👁
  1. not really. Try this:

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    U= { all positive integer less than or equal to 30} M={all even positive numbers less than or equal to 20} N={all odd number less than or equal to 19} S={all integer x: 10

  2. Math

    Tell whether the difference between the two integers is always, sometimes, or never positive. 1)Two positive integers. Never 2)Two negative integers. Sometimes. 3)A positive integer and a negative integer. Sometimes. 4)A negative

  3. Math

    Let z be a complex number, and let n be a positive integer such that z^n = (z + 1)^n = 1. Prove that n is divisible by 6. I have no idea how to approach this problem!

  4. 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 =

  1. Math

    When you add a positive integer and a negative integer, you sometimes get a negative result and sometimes get a positive result. Is the same true when you multiply a positive integer and a negative integer?

  2. math

    Which statement is true? A.The sum of two positive integers is sometimes positive, sometimes negative. B.The sum of two negative integers is always negative. C.The sum of a positive integer and a negative integer is always

  3. Math (Proof)

    Prove that if ab = ac (mod n) and a is relatively prime to n, then b = c (mod n). Proof: a and n are relatively prime and from ab = ac(mod n), we have n|(ab-ac), so n|a(b-c). Since (a,n)=1 (relatively prime), we get n(b-c). hence

  4. math

    prove that for any positive integer n, the value of 3^2n+2 - 8n-9 is divisible by 64

  1. probability

    how do we find the least residue of 1789 (mod 4), (mod 10), (mod 101)

  2. Maths

    Please help with these questions: (please show how to do) 1. How many differently shaped rectangles, with positive integer dimensions, have a perimeter equal to their area? 2. Let x be any number less than one, and let y be any

  3. math

    Show that any positive odd integer is of the form 6q+1, 6q+3 or 6q+5, where q is any positive integer

  4. maths

    can you answer this question: 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. with out using this method at all ................................. We

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