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Results tagged with diophantine-equations
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user 88319
Diophantine equations are polynomial equations $F=0$, or systems of polynomial equations $F_1=\ldots=F_k=0$, where $F,F_1,\ldots,F_k$ are polynomials in either $\mathbb{Z}[X_1,\ldots,X_n]$ of $\mathbb{Q}[X_1,\ldots,X_n]$ of which it is asked to find solutions over $\mathbb{Z}$ or $\mathbb{Q}$. Topics: Pell equations, quadratic forms, elliptic curves, abelian varieties, hyperelliptic curves, Thue equations, normic forms, K3 surfaces ...
2
votes
0
answers
187
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Solution of the Diophantine equation $x^4+y^4+z^4=2t^4$ are well-known? [closed]
Are solutions of the Diophantine equation $x^4+y^4+z^4=2t^4$ well-known?
I give a solution:
$x=m^2-n^2, y=m^2-2mn, z=n^2-2mn, t=m^2+n^2-mn$
- 477
-4
votes
2
answers
272
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Has nontrivial solution in positive integers of a diophantine equation: $x_1^2+x_2^2+x_3^2+x... [closed]
Has nontrivial solution in positive integers of a diophantine equation as follows ?
$$x_1^2+x_2^2+x_3^2+x_4^2=y_1^2+y_2^2+y_3^2+y_4^2$$
Where trivial solutions are $x_i=y_j$.
Can you send me any re …
- 477
4
votes
1
answer
587
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Another conjecture on sum $A+B=C$
Could You give your ideas, your comment, or a referen for a conjecture as follows:
Consider $A, B, C$ be three positive integers numbers. By Fundamental theorem of arithmetic we write:
$A=a_1^{ …
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