# Questions tagged [number-theory]

A field of mathematics studying numbers, their properties and structures that arise from them.

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### Source for a story about algebraic number theory?

I once read that Hilbert and Hurwitz (I think it was them) once discussed the theorem about unique factorization of ideals/divisors in algebraic number fields in one of their walks. They, the story ...
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1 vote
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### Why Did Riemann Venture into Number Theory for the Riemann Hypothesis?

I’m exploring the history behind the Riemann Hypothesis and I found something interesting. We know that Bernhard Riemann was mainly focused on complex analysis, but he also wrote a very important ...
2k views

### Who was Nicolò Paganini that discovered the amicable pair 1184, 1210?

Nicolò Paganini (not the violinist) was a 16 yo Italian schoolboy when he discovered that 1184 and 1210 form a pair of amicable numbers. It is in fact, the 2nd smallest such pair, and it did escape ...
659 views

### Where did Lagrange prove the Four Squares Theorem?

I am trying to confirm the initial publication of Lagrange's Four Squares Theorem. Most of my sources give that it was proved by him in $1770$. However, the generally very good Penguin Dictionary of ...
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1 vote
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### Finite fields as quotients

Although finite fields are usually introduced as field extensions of fields of prime order, they also arise as quotients of number rings; e.g., $GF(9)$ comes from taking the Gaussian integers mod 3 ...
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### Any historical work on the distribution of prime gaps?

I am looking to see whether historic mathematicians did any work to explain the slightly unexpected distribution of prime gaps? I would have expected Gauss, who studied lists of primes and proposed a ...
• 415
1 vote
156 views

### Euler's proof of infinite primes first since Euclid?

Q. Is it true that Euler's proof of infinite primes was the first since Euclid's which was from around 300BC? Note: By Euler's proof, I mean the use of his Euler product formula for the zeta function ...
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4k views

### Is the story about Fermat's writing on a margin true?

Is there any evidence that Fermat wrote on the margin of a book "I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." Everyone ...
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### What changes in mathematics resulted in the change of the definition of primes and exclusion of 1?

Why 1 is not prime? I read in this article that G.H Hardy explicitly included 1 as a prime in the first 6 editions of "A Course in Pure Mathematics", published between 1908-1933. He updated ...
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