Question 24
Prove that the number of 5-tuples of positive integers $(a, b, c, d, e)$ satisfying the equation
$$
a b c d e = 5(b c d e + a c d e + a b d e + a b c e + a b c d)
$$
is an odd integer.
$$
a b c d e = 5(b c d e + a c d e + a b d e + a b c e + a b c d)
$$
is an odd integer.