Question 81
Given positive integers $a$, $b$, $c$ and $d$ and
$$ (a+b)(a+c)(a+d)(b+c)(b+d)(c+d) = u, $$
$$ ab + ac + ad + bc + bd + cd = v, $$
prove that the product $uv$ is divisible by 3.
$$ (a+b)(a+c)(a+d)(b+c)(b+d)(c+d) = u, $$
$$ ab + ac + ad + bc + bd + cd = v, $$
prove that the product $uv$ is divisible by 3.