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In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is not mentioned, the field of rational numbers is generally understood. If the field is the field of real numbers, a rational point is more commonly called a real point. Understanding rational points is a central goal of number theory and Diophantine geometry. For example, Fermat's Last Theorem may be restated as: for n > 2, the Fermat curve of equation has no other rational points than (1, 0), (0, 1), and, if n is even, (–1, 0) and (0, –1).

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  • Point rationnel (fr)
  • 有理点 (ja)
  • 유리점 (ko)
  • Rational point (en)
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  • En théorie des nombres et géométrie algébrique, les points rationnels d'une variété algébrique définie sur un corps sont, lorsque X est définie par un système d'équations polynomiales, les solutions dans k de ce système. (fr)
  • In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is not mentioned, the field of rational numbers is generally understood. If the field is the field of real numbers, a rational point is more commonly called a real point. Understanding rational points is a central goal of number theory and Diophantine geometry. For example, Fermat's Last Theorem may be restated as: for n > 2, the Fermat curve of equation has no other rational points than (1, 0), (0, 1), and, if n is even, (–1, 0) and (0, –1). (en)
  • 数論において有理点(ゆうりてん、英: rational point)とは、各座標の値が全て有理数であるような空間の点のことである。 例えば、点 (3, −67/4) は 3 も −67/4 も有理数であるため、2次元空間内の有理点である。有理点の特別な場合として(integer point)があり、これは座標値が全て整数の点である。例えば、(1, −5, 0) は 3次元空間内の整数点である。より一般に K を任意の体とするとき、K-有理点は点の各々の座標値が体 K に属するような点と定義される。同様に、特別な場合である K-整数点は、各座標値が数体 K 内の代数的整数の環の元である点と定義される。 (ja)
  • 대수적 수론과 대수기하학에서, 대수다양체 또는 스킴의 유리점(有理點, 영어: rational point)은 좌표가 모두 유리수인 점이다. (ko)
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