Given any linear homogeneous Diophantine equation all points $(\alpha, \beta)$ on that line forms an infinite Abelian Group.But do there exist any operation that can turn it into a field ? I tried to think of multiplication like operation in that group. But $(\alpha_{1} \alpha_2, \beta_{1} \beta_2)$ is a point in another line (which is a different group). Is there any way to embed this field into some field ?
2026-05-06 10:30:52.1778063452
Field of coordinates in Diophantine equation
27 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in FIELD-THEORY
- Square classes of a real closed field
- Question about existence of Galois extension
- Proving addition is associative in $\mathbb{R}$
- Two minor questions about a transcendental number over $\Bbb Q$
- Is it possible for an infinite field that does not contain a subfield isomorphic to $\Bbb Q$?
- Proving that the fraction field of a $k[x,y]/(f)$ is isomorphic to $k(t)$
- Finding a generator of GF(16)*
- Operator notation for arbitrary fields
- Studying the $F[x]/\langle p(x)\rangle$ when $p(x)$ is any degree.
- Proof of normal basis theorem for finite fields
Related Questions in DIOPHANTINE-EQUATIONS
- Can we find $n$ Pythagorean triples with a common leg for any $n$?
- Can we find integers $x$ and $y$ such that $f,g,h$ are strictely positive integers
- Count of possible money splits
- I'm having a problem interpreting and starting this problem with primes.
- Solution of $X^5=5 Y (Y+1)+1$ in integers.
- Solving for 4 variables using only 2 equations
- Algorithm for diophantine equation
- Find all pairs of integers (x,y) such that $x(x+1)(x^2+x+2)=2y^2$
- Sum Equals Product: A Diophantine Equation
- Diophantine equation for Multivariate Polynomial
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?