Diophantine Equation in a sentence
(1) Fermat's Last Theorem is a famous Diophantine equation.
(2) The equation 3x + 5y = 7 is a simple Diophantine equation.
(3) The equation 2x + 3y = 5 is a linear Diophantine equation.
(4) The Diophantine equation x^2 - y^2 = 1 represents hyperbolas.
(5) The Diophantine equation 3x + 5y = 1 has no integer solutions.
(6) The Diophantine equation 5x + 8y = 2 has no integer solutions.
(7) The Diophantine equation 2x + 5y = 1 has no integer solutions.
(8) The Diophantine equation 3x + 5y = 7 has no integer solutions.
(9) The Diophantine equation 5x + 7y = 2 has no integer solutions.
(10) The Diophantine equation 4x + 5y = 3 has no integer solutions.
Diophantine Equation sentence
(11) The Diophantine equation 8x + 9y = 7 has no integer solutions.
(12) The equation x^4 + y^4 = z^4 is a quartic Diophantine equation.
(13) The equation x^2 - 2y^2 = 1 is a quadratic Diophantine equation.
(14) The Diophantine equation x^3 + y^3 = 1 represents elliptic curves.
(15) The equation x^2 + y^2 = z^2 is a well-known Diophantine equation.
(16) The equation x^3 + y^3 + z^3 = 33 is a cubic Diophantine equation.
(17) Solving a Diophantine equation requires finding integer solutions.
(18) The Diophantine equation 4x + 7y = 3 has a unique integer solution.
(19) The Diophantine equation 3x + 4y = 7 has a unique integer solution.
(20) The Diophantine equation 2x + 3y = 5 has a unique integer solution.
Diophantine Equation make sentence
(21) The Diophantine equation 4x + 7y = 1 has a unique integer solution.
(22) The Diophantine equation 3x + 4y = 5 has a unique integer solution.
(23) The Diophantine equation 6x + 9y = 12 has a unique integer solution.
(24) The Diophantine equation 2x + 3y = 10 has multiple integer solutions.
(25) The Diophantine equation 9x + 10y = 11 has a unique integer solution.
(26) The Diophantine equation x^3 + y^3 = z^3 is known as the Fermat cubic.
(27) The Diophantine equation x^2 + y^2 = z^2 represents Pythagorean triples.
(28) Solving a Diophantine equation often involves finding integer solutions.
(29) The Diophantine equation x^2 - 2y^2 = 1 is an example of a Pell equation.
(30) The Diophantine equation 3x + 6y + 9z = 15 has a unique integer solution.
Sentence of diophantine equation
(31) A Diophantine equation is a polynomial equation with integer coefficients.
(32) The Diophantine equation x^2 + y^2 = 10z^2 represents Pythagorean triples.
(33) The equation x^3 + y^3 = z^3 is another example of a Diophantine equation.
(34) The Diophantine equation 3x + 6y = 9 has infinitely many integer solutions.
(35) The Diophantine equation 2x + 3y = 1 has infinitely many integer solutions.
(36) The Diophantine equation 2x + 5y = 3 has infinitely many integer solutions.
(37) The Diophantine equation x^2 + y^2 = 7z^2 represents Pythagorean septuples.
(38) The Diophantine equation 7x + 8y = 9 has infinitely many integer solutions.
(39) The Diophantine equation 5x + 6y = 4 has infinitely many integer solutions.
(40) The Diophantine equation 2x + 4y = 12 has infinitely many integer solutions.
Diophantine Equation meaningful sentence
(41) The Diophantine equation x^2 + y^2 = 5z^2 represents Pythagorean quintuples.
(42) The Diophantine equation x^2 + y^2 = 11z^2 represents Pythagorean undecuples.
(43) The Diophantine equation 2x + 3y + 5z = 20 has infinitely many integer solutions.
(44) The Diophantine equation x^3 + y^3 = 2z^3 is an example of a cubic Thue equation.
(45) The Diophantine equation 2x + 3y + 5z = 10 has infinitely many integer solutions.
(46) The Diophantine equation x^2 - 3y^2 = 1 is an example of a negative Pell equation.
(47) The Diophantine equation x^2 + y^2 = 5z^2 represents primitive Pythagorean triples.
(48) The Diophantine equation x^3 + y^3 = z^3 is known as the Fermat-Catalan conjecture.
(49) Solving a Diophantine equation involves finding integer solutions for the variables.
(50) The Diophantine equation x^2 - 4y^2 = 1 is an example of a hyperbolic Pell equation.
Diophantine Equation sentence examples
(51) The Diophantine equation x^3 + y^3 + z^3 = 3w^3 is known as the Euler quartic conjecture.
(52) The Diophantine equation x^3 + y^3 + z^3 = 4w^3 is an example of a quartic Thue equation.
(53) Fermat's Last Theorem is a famous Diophantine equation that remained unsolved for centuries.
(54) The equation x^2 + y^2 = 10z^2 is an example of a Diophantine equation with a square number.
(55) The Diophantine equation x^3 + y^3 + z^3 + w^3 = 6u^3 is an example of a quintic Thue equation.
(56) The Diophantine equation x^3 + y^3 + z^3 + w^3 = 5u^3 is known as the Davenport-Cassels theorem.
(57) Hilbert's tenth problem asks for an algorithm to determine if a given Diophantine equation has integer solutions.
Diophantine Equation meaning
Diophantine equation is a term that refers to a specific type of mathematical equation, named after the ancient Greek mathematician Diophantus. These equations involve finding integer solutions for polynomial equations with multiple variables. If you are looking to incorporate the term "Diophantine equation" into your writing, here are some tips on how to use it effectively in a sentence:
1. Definition and Context: Begin by providing a brief definition or explanation of what a Diophantine equation is.
For example, "A Diophantine equation is a polynomial equation with integer solutions, named after the Greek mathematician Diophantus."
2. Historical Background: To add depth to your sentence, you can mention the historical significance of Diophantine equations. For instance, "Diophantine equations have been studied since ancient times, with Diophantus being one of the first mathematicians to explore their properties."
3. Mathematical Application: Highlight the practical applications of Diophantine equations in various fields.
For example, "Diophantine equations find applications in cryptography, number theory, and computer science, making them a crucial tool in modern mathematics."
4. Example Sentence: Provide an example sentence that demonstrates the correct usage of the term. For instance, "The mathematician used a Diophantine equation to solve the problem, finding the integer solutions that satisfied the given polynomial equation."
5. Related Terminology: Include related terms or concepts that are associated with Diophantine equations. This can help readers understand the broader context. For instance, "Diophantine equations are closely related to modular arithmetic and congruence relations, as they often involve finding solutions within a specific modulus."
6. Historical Contributions: Discuss the contributions made by Diophantus and other mathematicians in the field of Diophantine equations.
For example, "Diophantus' work on Diophantine equations laid the foundation for future mathematicians, such as Pierre de Fermat, who famously proposed Fermat's Last Theorem, a problem related to Diophantine equations."
7. Challenges and Complexity: Acknowledge the complexity and challenges associated with solving Diophantine equations. For instance, "Diophantine equations are known for their difficulty, as finding integer solutions can be a complex task, often requiring advanced mathematical techniques."
8. Modern Research: Mention any recent advancements or ongoing research related to Diophantine equations. This demonstrates that the field is still active and evolving.
For example, "Contemporary mathematicians continue to explore Diophantine equations, with recent research focusing on developing efficient algorithms for solving them."
9. Importance in Problem-Solving: Highlight the importance of Diophantine equations in problem-solving and their role in advancing mathematical knowledge. For instance, "Diophantine equations provide a framework for solving real-world problems that involve finding integer solutions, making them an essential tool for mathematicians and scientists alike."
10. Conclusion: Wrap up your sentence by summarizing the significance of Diophantine equations.
For example, "
In conclusion, Diophantine equations play a crucial role in mathematics, offering a means to solve complex problems and contributing to the development of various fields." By following these tips, you can effectively incorporate the term "Diophantine equation" into your writing, providing a comprehensive understanding of its meaning and significance.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Diophantine Equation. They do not represent the opinions of TranslateEN.com.