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MathNet 2003 — Part 01 Question 193

Math Olympiad Vault · MathNet 2003 — Part 01

Question 193

Three positive integers $a, b, c$ are given. Given $x = a b$, $y = a c$, $z = b c$, which of the following statements is true?
  1. If $x, y, z$ are squares, then $a, b, c$ are squares
  2. if $x, y, z$ are even, then $a, b, c$ are even
  3. if $x, y, z$ are cubes, then $a, b, c$ are cubes
  4. if $x, y, z$ are multiples of 10, then $a, b, c$ are multiples of 10
  5. none of the above statements are correct.