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That is the logic behind selecting even square root for fe_sqrtm1 = sqrt(-1)

x = sqrt(-1)

x = 547cdb7fb03e20f4d4b2ff66c2042858d0bce7f952d01b873b11e4d8b5f15f3d
x = 2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0

Value 2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0 is used here: https://github.com/monero-project/monero/blob/v0.17.1.9/src/crypto/crypto-ops-data.c#L38

0

I believe you'll find that it's the positive (as opposed to "even"), that's chosen (by convention). The positive one has the sign-bit set as 0.

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