Questions tagged [diophantine-equation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
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
vote
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,...
0
votes
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 ...