The collection of prime powers can be characterized in the following way: There is a field with $q$ elements if and only if $q$ is a prime power. Furthermore if it exists then this field is unique ...
Irreducible polynomials are often introduced as the analog to prime numbers in polynomial rings. Prime numbers, of course, have a very rich theory, leading to the likes of the Riemann Zeta function ...
Hello, My question is about the non-standard models of the integers. If we add to the Peano's axioms $P$ of arithmetic the following axioms for a fixed constant $c$: $c \neq 0$, $c \neq 1$, $c \neq ...
In their famous 'Primes is in P' paper Agrawal, Kayal and Saxena stated the following conjecture: If for coprime integers $n$ and $r$ the equality $(X-1)^n = X^n - 1$ holds in ...
It is well-known that there exists a (justly celebrated) topological proof of the infinitude of primes (Hillel Fürstenburg, 1955). Does there also exist an algebraic proof?
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 ...