BG-MO 1992 Problem 4

Let $p$ be a prime number in the form $p=4k+3$ . Prove that if the numbers $x_0,y_0,z_0,t_0$ are solutions of the equation $x^{2p}+y^{2p}+z^{2p}=t^{2p}$ , then at least one of them is divisible by $p$ . (Plamen Koshlukov)