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A Diophantine equation is an algebraic equation where only integer solutions are allowed. These equations are named after the ancient Greek mathematician Diophantus of Alexandria, who studied them extensively. They are used in number theory and have applications in cryptography and computer science.
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His name was actually Diophantus. The Diophantine equation was named after his work with similar problems dealing with how to solve quadratic equations.
- He was the first mathematician to recognize fractions as positive inetegers.
- He wrote Arithmetica, one of the first books on algebra.
He was considered the father of algebra.
In mathematics, a Diophantine equation (named for Diophantus of Alexandria, a third century Greek mathematician) is a polynomial equation where the variables can only take on integer values. Although you may not realize it, you have seen Diophantine equations before: one of the most famous Diophantine equations is:
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A Diophantine Equation. In order to solve it, you should use Euclide's algorithm.
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To solve a diophantin equation using python, you have to put it into algebraic form. Then you find out if A and B have a common factor. If they have a common factor, then you simplify the equation. You then build a three row table and build the table.
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Wolfgang M. Schmidt has written:
'Lectures on irregularities of distribution' -- subject(s): Irregularities of distribution (Number theory)
'Analytischme Methoden F Ur Diophantische Gleichugen'
'Equations over finite fields' -- subject(s): Finite fields (Algebra), Diophantine analysis
'Approximation to algebraic numbers' -- subject(s): Algebraic fields, Approximation theory, Diophantine analysis, International Mathematical Union
'Diophantine approximations and diophantine equations' -- subject(s): Diophantine approximation, Diophantine equations
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James Matteson has written:
'A collection of Diophantine problems with solutions' -- subject(s): Diophantine analysis
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R. C. Mason has written:
'Diophantineequations over function fields' -- subject(s): Algebraic fields, Diophantine analysis, Diophantine equations
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Matthew Collins has written:
'A tract on the possible and impossible cases of quadratic duplicate equalities in the Diophantine analysis' -- subject(s): Diophantine analysis, Forms, Quadratic, Quadratic Forms
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Thanks to the contributors at Wikipedia here is the answer...
Equations can be classified according to the types of operations and quantities involved. Important types include:
- An algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
- A linear equation is an algebraic equation of degree one.
- A polynomial equation is an equation in which a polynomial is set equal to another polynomial.
- A transcendental equation is an equation involving a transcendental function of one of its variables.
- A functional equation is an equation in which the unknowns are functions rather than simple quantities.
- A differential equation is an equation involving derivatives.
- An integral equation is an equation involving integrals.
- A Diophantine equation is an equation where the unknowns are required to be integers.
- A quadratic equation
To learn more click on the Wikipedia Link in the sources and references section below.
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To make 1 pound using 50p, 20p, and 10p coins, we can set up an equation: 50x + 20y + 10z = 100, where x, y, and z represent the number of each coin. We need to find all possible combinations of x, y, and z that satisfy this equation. This is a problem of Diophantine equations, specifically the Frobenius coin problem, which can be solved using techniques such as generating functions or linear Diophantine equations methods. The number of ways to make 1 pound with these coins would depend on the specific values of x, y, and z that satisfy the equation.
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The solution to this is equivalent to solving the linear diophantine equation 2x+6y=7 It is known that this equation has a solution if and only if the gcd of (2,6) divides 7 Since (2,6)=2 and 2 does not divide 7 there is no solution and it cannot be done.
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Diophantine equations have integral (ordinal scale) results.
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First of all I am not sure what you are asking? Do you mean 2x-3y=19? If so, you probably want two equations in two unknowns. Unless you are asking about a linear diophantine equation? So please clarify... Dr. Chuck
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Adler has written:
'Existential formulas in arithmetic' -- subject(s): Recursive functions, Diophantine analysis
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Robert Daniel Carmichael has written:
'The theory of numbers, and Diophantine analysis' -- subject(s): Diophantine analysis, Number theory
'A debate on the theory of relativity, with an introduction by William Lowe Bryan, favoring the theory' -- subject(s): Relativity (Physics)
'The theory of numbers' -- subject(s): Accessible book, Number theory
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To make a pound using only 50p, 20p, and 10p coins, we can set up a linear Diophantine equation: 50x + 20y + 10z = 100, where x, y, and z are the number of each type of coin used. We can then use techniques such as generating functions or modular arithmetic to solve this equation and find the number of ways to make a pound. The solution will involve finding the integer solutions to the equation within a certain range, as there are constraints on the number of each type of coin available.
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Diophantine approximation deals with approximation to real numbers by rational numbers. The symbol "≈" means "approximately equal to"; tilde (~) and the Libra sign () are common alternatives.
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Wilhelm Ljunggren has written:
'Collected papers of Wilhelm Ljunggren' -- subject(s): Diophantine equations, Number theory, Quadratic Forms
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..i think its diphantus..he is a greek mathematician..he lived in alexandria,egypt,where he occupied himselfcheifly with diophantine analysis,earning the the litle father of algebra...he wrote the arithmethicca, of which only 6 out of 13 was sold.....
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It is an equation. It could be an algebraic equation, or a trigonometric equation, a differential equation or whatever, but it is still an equation.
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Simply that, an "equation".
Simply that, an "equation".
Simply that, an "equation".
Simply that, an "equation".
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A logarithmic equation would be any equation that includes the log function.
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numbers are equation because there are numbers in equation which make numbers equation
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Scienitifc equation is a equation that has lots of scientifical things
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Such an equation is called a "proportion".
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If this value a satisfy the equation, then a is a solution for that equation. ( or we can say that for the value a the equation is true)
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"Figure out this mathematical equation"
"This is how to figure out an equation"
"An equation is something widely used in mathematics."
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It is the solution to the equation or a root of the equation.
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To write an equation that includes the keyword "how to write an equation," you can use a variable like x to represent the phrase. For example, the equation could be x "how to write an equation."
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AX + BY is not an equation .
AX + BY + C = 0
is the general equation for a straight line.
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An Airy equation is an equation in mathematics, the simplest second-order linear differential equation with a turning point.
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Solution. A solution of an equation is a number that satisfy the equation. This means that if you replace this number on the equation and check it, the equation will be true.
When you solve an equation you can find some roots, but not all of them satisfy the equation. Thus always check your answers after resolving your equation, and eliminate as solution the answers that don't make the equation true or undefined.
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You find the equation of a graph by finding an equation with a graph.
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The graph of an equation is a visual representation of the values that satisfy the equation.
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An equation is equivalent to another equation, if they have the same solution.
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Plot the solution of the equation for various variables in the equation
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Equation 7 is not an equation and so cannot have a slope.
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Such an equation is called an IDENTITY.
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