diophantine equation examples The questions asked in Diophantine analysis include 1 Are there any solutions 2 Are there any solutions beyond some that are easily found by inspection 3 Are there finitely or infinitely many solutions
With a Diophantine Equation we are only interested in integer solutions Puzzles A Diophantine Equation is basically a puzzle can you find integer solutions to a certain equation A Diophantine equation is a polynomial equation whose solutions are restricted to integers These types of equations are named after the ancient Greek mathematician Diophantus A linear Diophantine equation is a first degree
diophantine equation examples
diophantine equation examples
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Example 8 19 A Linear Diophantine Equation in Two Variables The following example is similar to the examples studied in Preview Activity PageIndex 2 We can use The most famous diophantine equation is the Fermat equation xd yd zd 0 For d 2 there are many integer solutions and for d 3 there are no positive integer solutions
Ax by c It is Linear because the variables x and y have no exponents such as x 2 etc And it is Diophantine because of Diophantus who loved playing with integers Example Sam sold some A Diophantine equation is an equation relating integer or sometimes natural number or whole number quanitites Finding the solution or solutions to a Diophantine equation is closely tied
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Learn about Diophantine equations a class of polynomial equations that have integer solutions See examples tricks theorems and problems with solutions involving factoring modular These are the most popular such equations to solve Linear Diophantine equations ax by c Pythagorean Triples x2 y2 z2 Fermat s Last Theorem xn yn zn for n 2 Pell s equation x2 ny2 1 The Erd s Straus conjecture 4n 1x 1y 1z Taxicab numbers w3 x3 y3 z3
Here is a fairly arbitrary selection of examples of Diophantine Equations 1 aX bY c with given a b c2Z we are looking for solutions X Y 2Z there are always rational solutions unless Diophantine equation named after Diophantus of Alexandria right is a polynomial equation with integer coe cients that is intended to be solved with integer solu tions You may have never
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diophantine equation examples - A Diophantine equation is an equation relating integer or sometimes natural number or whole number quanitites Finding the solution or solutions to a Diophantine equation is closely tied