“Diophantine equation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Diophantine equation

释义

Diophantine equation

In number theory, an algebraic equation in one or more unknowns, with integer coefficients, for which integer solutions are sought. As examples:

(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 only trivial solutions.

See also Catalan's conjecture, Fermat's last theorem, Hilbert's tenth problem, Pell's equation.

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