# Tagged Questions

**4**

votes

**4**answers

899 views

### Is there an analogue of finite fields for products of two prime powers?

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 ...

**0**

votes

**1**answer

386 views

### Primes are to Irreducible Polynomials as Prime-related theorems are to ?? [closed]

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 ...

**9**

votes

**2**answers

849 views

### Non-Standard Prime

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 ...

**28**

votes

**3**answers

2k views

### What is the current status of Agrawal's conjecture?

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 ...

**2**

votes

**1**answer

1k views

### Is there an algebraic proof of the infinitude of primes? [closed]

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?

**10**

votes

**2**answers

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 ...