18
votes
1answer
1k views

The Quaternion Moat Problem

"One cannot walk to infinity on the real line if one uses steps of bounded length and steps on the prime numbers. This is simply a restatement of the classic result that there are arbitrarily large ...
10
votes
2answers
1k views

Gaussian primes, quaternion primes, … octonions?

Is there a notion of an octonion prime? A Gaussian integer $a + bi$ with $a$ and $b$ nonzero is prime if $a^2 + b^2$ is prime. A quaternion $a + bi + cj + dk$ is prime iff $a^2 + b^2 +c^2 + d^2$ is ...