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Results tagged with nt.number-theory
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user 5043
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
21
votes
2
answers
2k
views
For $x,y\ge 2$ does $x^4+x^2y^2+y^4$ ever divide $x^4y^4+x^2y^2+1$?
For a problem in combinatorics, it comes down to knowing whether there exist integers $x,y\ge 2$ such that
$$
x^4+x^2y^2+y^4\mid x^4y^4+x^2y^2+1.
$$
Note that $x^6(x^2-y^2)(x^4+x^2y^2+y^4)+(x^2y^2-1 …
- 623
18
votes
1
answer
2k
views
A geometric series equalling a power of an integer
The following problem cropped up whilst considering generalised quadrangles with a product structure, and it boils down to a simple number theoretic problem. Let $s$ be an integer greater than 2 and s …
- 623