The chakravala method (Sanskrit: चक्रवाल विधि) is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. It is commonly...

William Brouncker in 1657, though his method was more difficult than the chakravala method. The first general method for finding the solutions of the problem...

equations. Bhaskara II is generally credited with developing the chakravala method, building on the work of Jayadeva and Brahmagupta. Solutions to specific...

publications, including an article on the Chakravala method where he showed how the method differed from the method of continued fractions. He pointed out...

was an Indian mathematician, who further developed the cyclic method (Chakravala method) that was called by Hermann Hankel "the finest thing achieved...

Apollonius, two of the greatest minds produced by antiquity." Chakravala method – The Chakravala method, a cyclic algorithm to solve indeterminate quadratic equations...

to have been made during classical antiquity in Europe. Chakravala method: The Chakravala method, a cyclic algorithm to solve indeterminate quadratic equations...

square root is not rational.) For that matter, the eleventh-century chakravala method amounts—in modern terms—to an algorithm for finding the units of a...

equation in positive integers is x = 226153980, y = 1766319049 (see Chakravala method). In 1900, David Hilbert proposed the solvability of all Diophantine...

solution (including zero and negative solutions) to quadratic equations. Chakravala method, sign convention, madhava series, and the sine and cosine in trigonometric...

of Pell's equation using the chakravala method. The general indeterminate quadratic equation using the chakravala method. Indeterminate cubic equations...

calculations that can also be applied to multiplication. The method for general multiplication is a method to achieve multiplications a × b {\displaystyle a\times...

Efficient way of calculating GCD. Booth's multiplication algorithm Chakravala method: a cyclic algorithm to solve indeterminate quadratic equations, including...

apsidal precession of the Sun. 12th century: Bhāskara II develops the Chakravala method, solving Pell's equation. 12th century: Al-Tusi develops a numerical...

identity Brahmagupta's formula Brahmagupta theorem Brahmagupta triangle Chakravala method List of Indian mathematicians History of science and technology on...

Indian mathematician who wrote an article on the difference between Chakravala method and Continued Fractions. Ashutosh Mukherjee, Indian mathematician...

Eratosthenes 263 AD – Gaussian elimination described by Liu Hui 628 – Chakravala method described by Brahmagupta c. 820 – Al-Khawarizmi described algorithms...

positive number has two square roots. Furthermore, it also gives the Chakravala method which was the first generalized solution of so-called Pell's equation...

were extended to a complete solution of Pell's equation known as the chakravala method, attributed to either of the Indian mathematicians Jayadeva or Bhāskara...

Bhaskara's Lemma is an identity used as a lemma during the chakravala method. It states that: N x 2 + k = y 2 ⟹ N ( m x + y k ) 2 + m 2 − N k = ( m y...

Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: N = a 2...

In number theory, Dixon's factorization method (also Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm;...

quadratic equations, including Pell's equation which is known as chakravala method or cyclic method. Bijaganita is the first text to recognize that a positive...

practice, the elliptic curve method is faster than the Pollard p − 1 method once the factors are at all large; running the p − 1 method up to B = 232 will find...

Euler's factorization method is a technique for factoring a number by writing it as a sum of two squares in two different ways. For example the number...

examples. Quadratic. 17 rules and 10 examples. Includes a variant of the Chakravala method. Ganita Kaumudi contains many results from continued fractions. In...

Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization...

table Pollard, John M. (July 1978) [1977-05-01, 1977-11-18]. "Monte Carlo Methods for Index Computation (mod p)" (PDF). Mathematics of Computation. 32 (143)...

non-performing restoring, non-restoring, and SRT division. Fast division methods start with a close approximation to the final quotient and produce twice...

, since divisibility by an even number implies divisibility by 2. This method can be improved further. Observe that all primes greater than 5 are of the...