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In some notes of mine I have found a comment according to which the Indian mathematician Narayana Pandit (14th century) found the prime factors of $1161$ by writing it in the form $1161 = 35^2-8^2$. U …

The parity conjecture for elliptic curves predicts that the rank of an elliptic curve defined over the rationals has the same parity as the p-Selmer rank for a prime number p. Could anyone familiar wi …

The Greeks knew that numbers of the form $\sqrt{n}$ for nonsquare integers $n$ are not rational. Much later, Lambert (1768) proved that the values of $e^x$ and $\tan x$ are irrational for nonzero rat …

It is well known that Euler gave the first proof of FLT ($x^n + y^n = z^n$ has no nontrivial integral solutions for $n > 2$) for exponent $n=3$, but that his proof had gaps (which are not as easily cl …

Leonardo of Pisa is best known as Fibonacci; various stories found in books and on the web claim that the name Fibonacci was invented by Edouard Lucas or Guillaume Libri in the 19th century, and that …

I am writing an article on Fermat's work in number theory and feel uncomfortable everytime I have to write "Fermat's Little Theorem": it's clumsy and belittles the fundamental character of Fermat's re …

I browsed Dirichlets Werke today and was kind of surprised by two remarks that he made on p. 354 (Über die Bestimmung ...) and p. 372 (Sur l'usage ...). In the second paper, he claims (my translation) …

Everybody knows that polynomial rings over fields have unique factorization, and that if $R$ has unique factorization, then so does $R[X]$. And everybody knows who proved these results first. Well, …

Consider the series $$ S_f = \sum_{x=1}^\infty \frac{f}{x^2+fx}. $$ Goldbach showed that, for integers $f \ge 1$, $$ S_f = 1 + \frac12 + \frac13 + \ldots + \frac1f $$ (this follows easily by writing …