IMO 1969 Q1 #
Prove that there are infinitely many natural numbers $a$ with the following property: the number $z = n^4 + a$ is not prime for any natural number $n$.
The key to the solution is that you can factor $z$ into the product of two polynomials,
if $a = 4*m^4$. This is Sophie Germain's identity, called
To show that the product is not prime, we need to show each of the factors is at least 2,
nlinarith can solve since they are each expressed as a sum of squares.
The factorization is over the integers, but we need the nonprimality over the natural numbers.