Prove that there exist infinitely many integers $x$ such that integer $P(x)=x^3-2$ is a sum of two squares of integers. Ideally, I am looking for a proof method that also applies for other $P(x)$, such as, for example, $P(x)=x^3+x+1$. For $x=4t+3$, $P=(4t+3)^3-2$ is $1$ modulo $4$. By a well-beli...

Recently the Billionaire Space Race culminated with both Jeff Bezos and Richard Branson, doing what I can tell without any dispute, "going up" and "coming down". The claim that either of them actually reached space however is hotly debated, with astrophysicist Neil deGrasse Tyson telling (paraphr...