How do you express "All pairs of integer have a greatest common divisor" in mathematical term?
This is what I came up with but I'm unsure if it's right.
Any help is appreciated, thanks!
2026-03-25 15:54:42.1774454082
How do you express "Every pair of integer has a greatest common divisor" in mathematical terms?
272 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PROPOSITIONAL-CALCULUS
- Help with Propositional Logic Proof
- Can we use the principle of Explosion to justify the definition of implication being True when the antecedent is False?
- Simplify $(P \wedge Q \wedge R)\vee(\neg P\wedge Q\wedge\neg R)\vee(\neg P\wedge\neg Q\wedge R)\vee(\neg P \wedge\neg Q\wedge\neg R)$
- Alternative theories regarding the differences between the material conditional and the indicative conditionals used in natural language?
- Translations into logical notation
- Is the negation of $(a\wedge\neg b) \to c = a \wedge\neg b \wedge\neg c$?
- I am kind of lost in what do I do from here in Propositional Logic Identities. Please help
- Boolean Functional completeness of 5 operator set in propositional logic
- Variables, Quantifiers, and Logic
- Comparison Propositional Logic
Related Questions in GCD-AND-LCM
- How do I show that if $\boldsymbol{a_1 a_2 a_3\cdots a_n \mid k}$ then each variable divides $\boldsymbol k $?
- GCD of common divisors in integral domain
- How do I solve this difficult gcd question?
- Fractions of the form $\frac{a}{k}\cdot\frac{b}{k}\cdot\frac{c}{k}\cdots=\frac{n}{k}$
- Why can't be a number the gcd of two numbers?
- Prove that if $\gcd(m, n) > 1$, then there do not exist integers $x, y$ so that $mx + ny = 1$.
- Least number of cuts to share sausages equally
- For $f \in \mathbb{Z}[x]$ , $\deg(\gcd_{\mathbb{Z}_q}(f, x^p - 1)) \geq \deg(\gcd_{\mathbb{Q}}(f, x^p - 1))$
- GCD as linear combination of two numbers
- A question regarding greatest common divisor
Related Questions in LOGIC-TRANSLATION
- Find the truth value of... empty set?
- Translating an English sentence into predicate logic
- Rewriting a statement in logical form
- Translating a statement into predicate logic
- Propositional Logic Formula
- How to denote "but not" in symbolic logic form?
- Having trouble with a translation in first-order logic
- Translating English to Propositional Logic for NOR
- Using quantifiers to translate sentences
- Compound proposition from Alice in Wonderland
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?
A correct statement is:
$$\forall x,y\left(\exists d\left(d\mid x\land d\mid y\land\forall e\left((e\mid x\land e\mid y)\Rightarrow e\leq d\right)\right)\right) $$
This is only true if your language is the positive integers.
If the language includes zero you need something like:
$$\forall x,y\left((x=0\land y=0)\lor\\\exists d\left(d\mid x\land d\mid y\land\forall e\left((e\mid x\land e\mid y)\Rightarrow e\leq d\right)\right)\right) $$