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Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

6 votes
1 answer
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Extension of Erdos-Selfridge Theorem

Erdos and Selfridge open their paper "The Product of Consecutive Integers is Never a Power" (1974) with the theorem $\text{Theorem 1:}$ The product of two or more consecutive positive integers is …
Matt Cuffaro's user avatar
5 votes

Connection Between Knot Theory and Number Theory

I recommend Chao Li/Charmaine Sia's notes for a brisk and illustrated overview of the ever-growing MKR dictionary detailed in Knots and Primes. The first three or so chapters of the source book is rat …
Matt Cuffaro's user avatar