06-17-2026, 10:18 PM
Pell’s equation is the Diophantine equation ($x^2 - Dy^2 = 1$), where (D) is a positive non-square integer and (x) and (y) are integers. Although named after the English mathematician John Pell, it was extensively studied centuries earlier by Indian mathematicians such as Brahmagupta and Bhaskara II.
The equation has infinitely many integer solutions whenever (D) is not a perfect square, and all solutions can be generated from a smallest nontrivial solution called the fundamental solution. Pell’s equation is closely connected to continued fractions, algebraic number theory, and the approximation of irrational numbers, making it a classic and important problem in number theory with deep historical and mathematical significance.
ARTICLE
The equation has infinitely many integer solutions whenever (D) is not a perfect square, and all solutions can be generated from a smallest nontrivial solution called the fundamental solution. Pell’s equation is closely connected to continued fractions, algebraic number theory, and the approximation of irrational numbers, making it a classic and important problem in number theory with deep historical and mathematical significance.
ARTICLE
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