Talk:Zolotarev's lemma

An example which isn't an example

The article currently says

This interpretation of the Legendre symbol as the sign of a permutation can be extended to the Jacobi symbol ... where a and n are relatively prime odd integers with n > 0: ... For example, multiplication by 2 on Z/21Z has cycle decomposition ... and the Jacobi symbol (2|21) is −1.

Since 2 is not an odd integer, this isn't an example of the extension which it says it's an example of. In fact, it seems to be an example of a still stronger generalisation. What's the correct statement of the extension? 95.17.84.95 (talk) 13:16, 8 December 2015 (UTC)[reply]

Another proof

To me it's unclear from where the author infers the assertion "But W is even, ..." in the last line of the proof. — MFH:Talk 20:49, 18 November 2020 (UTC)[reply]

Two answers

The remark on the incorrect example is correct. The proper statement requires only n to be odd.

W is even because it acts the same on each of the two rows in the matrix. 131.155.95.134 (talk) 08:19, 2 September 2021 (UTC)[reply]