# Tag: algebraic-number-theory

## modular arithmetic – Fibonacci number that ends with 2014 zeros?

The Question : 105 people think this question is useful This problem is giving me the hardest time: Prove or disprove that there is a Fibonacci number that ends with 2014 zeros. I tried mathematical induction (for stronger statement that claims that there is a Fibonacci number that ends in any number of zeroes), but

## number theory – Does every ring of integers sit inside a ring of integers that has a power basis?

The Question : 121 people think this question is useful Given a finite extension of the rationals, $K$, we know that $K=\mathbb{Q}[\alpha]$ by the primitive element theorem, so every $x \in K$ has the form $$x = a_0 + a_1 \alpha + \cdots + a_n \alpha^n,$$ with $a_i \in \mathbb{Q}$. However, the ring of integers,

## algebraic number theory – What’s the significance of Tate’s thesis?

The Question : 143 people think this question is useful I’ve just sat through several lectures that proved most of the results in Tate’s thesis: the self-duality of the adeles, the construction of “zeta functions” by integration, and the proof of the functional equation. However, while I was able to follow at least some of