Questions tagged [diophantine-equation]
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3
questions
0
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1answer
45 views
Euclidean algorithm - runtime in specific case
I'm going to solving many times this specific equations:
$$2^{x+y} \cdot c - a^{y} \cdot z = 1$$
in which $$a$$ can be equal to: $$-7,-5,-3,-1,1,3,5,7.$$ And $$x+y$$ will be equal to $$128.$$ It has ...
1
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2answers
52 views
Multivariate polynomials
Given a Diophantine equation $p(x_1,x_2,...,x_n)$,
Can I find a reduction from $\text{dioph}(\mathbb{N}) \leq \text{dioph}(\mathbb{N}_e)$?
$\mathbb{N}_e$ is the set of even numbers.
So I have to ...
1
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0answers
29 views
How do you solve a general linear diophantine equation in polynomial time (with minimization constraint)?
Given
$$
a_1 X_1 + \dots + a_n X_n = b
$$
where $a_i, b \in \Bbb{Z}$. How do you come up with a clearer picture of the solution set in polynomial time.
Also, what I really want is to do the above,...
