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Diophantine analysis

Diophantine Di`o*phan"tine, a. Originated or taught by Diophantus, the Greek writer on algebra. Diophantine analysis (Alg.), that branch of indeterminate analysis which has for its object the discovery of rational values that satisfy given equations containing squares or cubes; as, for example, to find values of x and y which make x^2 + y^2 an exact square.

Diophantine Di`o*phan"tine, a. Originated or taught by Diophantus, the Greek writer on algebra. Diophantine analysis (Alg.), that branch of indeterminate analysis which has for its object the discovery of rational values that satisfy given equations containing squares or cubes; as, for example, to find values of x and y which make x^2 + y^2 an exact square.

- algebra. The mathematical study of Diophantine problems that Diophantus initiated is now called Diophantine analysis. While individual equations present...

- advances in number theory, and the study of Diophantine equations ("Diophantine geometry") and of Diophantine approximations remain important areas of mathematical...

- recurrence relation for generating solutions to certain instances of Diophantine equations of the second degree such as Nx2 + 1 = y2 (called Pell's equation)...

- In mathematics, Diophantine geometry is the study of points of algebraic varieties with coordinates in the integers, rational numbers, and their generalizations...

- monkey and the coconuts is a mathematical puzzle in the field of Diophantine analysis involving five sailors and a monkey on a desert island who divide...

- described the abc conjecture as "the most important unsolved problem in Diophantine analysis". Various attempts to prove the abc conjecture were made, but none...

- techniques that originate from linear algebra or mathematical analysis. Algebra also studies Diophantine equations where the coefficients and solutions are integers...

- Introduction to Modular Forms (1976) Complex Analysis (1977) Cyclotomic Fields (1978) Elliptic Curves: Diophantine Analysis (1978) Modular Units (1981) with Dan...

- existence of parallels between the Nevanlinna theory of complex analysis, and diophantine analysis in the circle of ideas around the Mordell conjecture and abc...

- Fermatschen Satzes. Leipzig: Brandstetter. Carmichael RD (1915). Diophantine Analysis. New York: Wiley. van der Corput JG (1915). "Quelques formes quadratiques...

- advances in number theory, and the study of Diophantine equations ("Diophantine geometry") and of Diophantine approximations remain important areas of mathematical...

- recurrence relation for generating solutions to certain instances of Diophantine equations of the second degree such as Nx2 + 1 = y2 (called Pell's equation)...

- In mathematics, Diophantine geometry is the study of points of algebraic varieties with coordinates in the integers, rational numbers, and their generalizations...

- monkey and the coconuts is a mathematical puzzle in the field of Diophantine analysis involving five sailors and a monkey on a desert island who divide...

- described the abc conjecture as "the most important unsolved problem in Diophantine analysis". Various attempts to prove the abc conjecture were made, but none...

- techniques that originate from linear algebra or mathematical analysis. Algebra also studies Diophantine equations where the coefficients and solutions are integers...

- Introduction to Modular Forms (1976) Complex Analysis (1977) Cyclotomic Fields (1978) Elliptic Curves: Diophantine Analysis (1978) Modular Units (1981) with Dan...

- existence of parallels between the Nevanlinna theory of complex analysis, and diophantine analysis in the circle of ideas around the Mordell conjecture and abc...

- Fermatschen Satzes. Leipzig: Brandstetter. Carmichael RD (1915). Diophantine Analysis. New York: Wiley. van der Corput JG (1915). "Quelques formes quadratiques...

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