Tonelli Shanks Algorithm
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Tonelli Shanks Algorithm

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High Quality Content by WIKIPEDIA articles! The Tonelli Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used within modular arithmetic to solve a congruence of the form x^2 equiv n pmod p where n is a quadratic residue (mod p), and p is an odd prime.Tonelli Shanks cannot be used for composite moduli; finding square roots modulo composite numbers is a computational problem equivalent to integer factorization.An equivalent, but slightly more redundant version of this algorithm was developed by Alberto Tonelli in 1891. The version discussed here was developed independently by ...