![(GDR 2)^{IMO1}](/media/m/2/9/7/297013cf6faec13fe347ee1422fb3380.png)
Prove that there exist infinitely many natural numbers
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
with the following property: The number
![z = n^4 + a](/media/m/e/8/d/e8da5ccaa6240bd6c46671ab500d33f2.png)
is not prime for any natural number
%V0
$(GDR 2)^{IMO1}$ Prove that there exist infinitely many natural numbers $a$ with the following property: The number $z = n^4 + a$ is not prime for any natural number $n.$