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Results tagged with nt.number-theory
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user 490128
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
1
vote
Applications of the Chinese remainder theorem
I didn't read this obvious application yet in the other answers: if you want to solve a polynomial equation in $\Bbb{Z}/n\Bbb{Z}$ and you factorize $n=q_1\dots q_m$ via CRT, you can calculate the solu …
- 1,245
3
votes
2
answers
225
views
Integer solutions to $x^2 + x + 1 = y^z$? [duplicate]
In the context of finite projective planes I am interested in the Diophantine equation $\frac{x^3-1}{x-1} = y^z$, which is also written as $x^2 + x + 1 = y^z$, for $z>1$. I stumbled by accident on the …
- 8,842
5
votes
Find four natural numbers with a certain property
For four numbers, $2$, $3$, $7$ and $43$ do the job. In general, if $n$ is the amount of numbers and the product of all but one of them, say $T$, must be $-1$ modulo $T$, we can state the following:
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- 1,245