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September 22

Tonelli-Shanks extensions

How can the algorithm be extended to, for example, x^2 - x == n (mod p)? Or to any polynomial function of x? 68.0.144.214 (talk) 00:40, 22 September 2013 (UTC)[reply]

You can solve the quadratic equation in the usual way, division mod p is well defined, and when you have to take the square root, you have available the Tonelli-Shanks algorithm. Count Iblis (talk) 01:33, 22 September 2013 (UTC)[reply]

Rank and crank of a partition

I'm just starting to learn about this, and I see that the rank of a conjugate partition is the negative of the original rank, so in particlar, the rank of a selfconjugate partition is zero, and the selfconjugates are a subset of rank zero partitions, so i figured this skew-symmetry or odd-functionness with respect to conjugates would be important. But the crank doesn't have this property at all. Is there a way of tweaking the crank function to make it skew-symmetric? Thanks, Rich Peterson64.134.220.186 (talk) 20:27, 22 September 2013 (UTC)[reply]