Questions tagged [number-theory]

Questions on advanced topics - beyond those in typical introductory courses: higher degree algebraic number and function fields, Diophantine equations, geometry of numbers / lattices, quadratic forms, discontinuous groups and and automorphic forms, Diophantine approximation, transcendental numbers, elliptic curves and arithmetic algebra geometry, exponential and character sums, Zeta and L-functions, multiplicative and additive number theory, etc.

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3
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1answer
132 views
+50

Least period of functions

For $n$ coprime with $3$ define $v(n)$ as the number such that $n\equiv 2^{v(n)}\mod{27}$, and if $(n,3)>1$ define $v(n)=0$. With this we have $v(n)$ is periodic with least period $27$. \begin{...
26
votes
3answers
932 views
+100

Numbers that are the sum of the squares of their prime factors

A number which is equal to the sum of the squares of its prime factors with multiplicity: $16=2^2+2^2+2^2+2^2$ $27=3^2+3^2+3^2$ Are these the only two such numbers to exist? There has to be an easy ...
1
vote
0answers
97 views
+100

Equivalence of two version of the Central sets theorem.

I have seen two versions of the Central sets theorem. The first one, which is due to H. Furstenberg, is the following. Central sets theorem, version 1: Let $C$ be a central set in $\mathbb{N}$, and ...