Tagged Questions
2
votes
1answer
33 views
When is the complement of a diophantine set in the naturals also diophantine?
A diophantine polynomial is a (multivariable) polynomial with integer coefficients. If we write this polynomial as $p(x, y_1, \dots, y_n)$, then it defines the diophantine set $D_p = \{ x \in ...
1
vote
2answers
160 views
Solving an equation in modular arithmetic
Given $A, B, C$ positive integers, $B < C,$
I would like some thoughts about (possibly efficient) ways to find the
smallest integer $X$, where $0 < X < C$, such that:
$$A X + B \pmod{C - ...
1
vote
3answers
131 views
Does method exist to solve Diophantine/Algebraic equation with nearest integer variable?
Can anyone kindly tell me if there is a method (other than trial and error) to solve equations of the form below:
$$x^2 + x - 35 - 35[(x^2)/35] = 0$$
where $x$ is an integer and $[y]$ denotes the ...
3
votes
2answers
327 views
Algorithm to determine if a Diophantine Equation has an infinite number of solutions
In their paper , Marker and Slaman, proved the decidability of the the theory of the natural numbers with the quantifier "for all but finitely many", One can obviously encode the question of whether ...
3
votes
1answer
235 views
Diophantine equation and Turing Machine
If a Diophantine equation is: exists v, p(x,v) = 0 (where v is a vector of finitely many integers) for some polynomial p, is there a Turing machine which prints out all values of x?
