3 Integers.

Written on 11:32 pm by Vja Students

In how many ways can you choose 3 integers such that their sum and product have the same value and none of the 3 integers are equal?

Answer:
Infinite ways
{-a,0,-a}
3,2,1
-3,-2,-1

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3 Comments

  1. Net Esportes | 31 December 2007 at 1:01 am

    2 - 1 - 3 (this is a way)

     
  2. Unknown | 31 December 2007 at 7:49 am

    Guys, you have to be more careful with the question posing.

    There are infinite ways:
    (0,n,-n), among others.

    You probably meant: POSITIVE INTEGERS.

     
  3. Unknown | 31 December 2007 at 7:56 am

    Let a,b,c be three positive integers.

    If a,b >= 3; a + b + 1 << a*b.

    So c*a*b >> a + b + c. So we can assume two of them are smaller than 3 (repeat the argument for (b,c).

    Say 0 < a,b < 3. Then, since a and b must be different, they are exactly 1,2.

    So we have 1*2*c = 1 + 2 + c, or 2c = c + 3 => c = 3.

    So 1,2,3 is the only possibility for the reformulated problem.

     

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