All Questions
Tagged with k3-surfaces diophantine-equations
3
questions
12
votes
0
answers
698
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Why are solutions to $\sqrt[k]{x_1^k+x_2^k+x_3^k+x_4^k}$ for $k=2,3$ curiously smooth?
Given an integer solution $s_m$ to the system,
$$x_1^2+x_2^2+\dots+x_n^2 = y^2$$
$$x_1^3+x_2^3+\dots+x_n^3 = z^3$$
and define the function,
$$F(s_m) = x_1+x_2+\dots+x_n$$
For $n\geq3$, using an ...
- 11.8k
11
votes
1
answer
395
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Symmetric functions on three parameters being perfect squares
Is it possible for $x+y+z, xy+yz+zx$, and $xyz$ to be perfect squares at the same time for positive integer values of $x,y,z$?
- 1,045
3
votes
0
answers
390
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The surface $ x^2 y^2 + 1 = (x^2 + y^2) z^2 $
Hi, I'm trying to find all rational points on the surface of the title, in connection with the Euler Brick (AKA Rational Box) problem.
This surface is equivalent to $ x^2 z^2 - 1 = (x^2 - z^2) y^2 $, ...
- 1,495