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Diophantine equation


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An algebraic equation in one or more unknowns, with integer coefficients, for which integer solutions are required. A great variety of Diophantine equations have been studied. Some have infinitely many solutions, some have finitely many and some have no solutions. For example:(i) 14x+9y=1 has solutions x=2+9t, y=−3−14t (where t is any integer).(ii)x2+1=2y4 has two solutions x=1, y=1 and x=239, y=13.(iii)x3+y3=z3 has no solutions. See also Hilbert's tenth problem and Pell's equation.

(i) 14x+9y=1 has solutions x=2+9t, y=−3−14t (where t is any integer).

(ii)x2+1=2y4 has two solutions x=1, y=1 and x=239, y=13.

(iii)x3+y3=z3 has no solutions.

Subjects: Mathematics.


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