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Results tagged with nt.number-theory
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user 428
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
Accepted
Lifting bases for (Z/pZ)^n to Z^n
Here's a unified argument based on my comments to Scott's post that doesn't use quadratic reciprocity in any form. Suppose n=2 and p >= 5, and lift each line of slope i in Y(2,p) to a point (ai+pbi, …
- 6,589
28
votes
Accepted
Singmaster's conjecture
There is an upper bound of $O\left(\frac{(\log n)(\log \log \log n)}{(\log \log n)^3}\right)$ due to Daniel Kane: see "Improved bounds on the number of ways of expressing t as a binomial coefficient, …
- 6,589
17
votes
Accepted
Counting solutions to x^{p+1}=y^4 in a finite field
Let g be a generator of the multiplicative group of the field; assuming x and y are nonzero, we can write x=ga and y=gb with 0 <= a,b < p2-1, and then xp+1=y4 becomes ga(p+1)=g4b, or equivalently a(p+ …
- 6,589