PowerModList

Every in with — and so the place these units already live: the split units of are , its imaginary units .

Wolfram LanguagePowerModList✓

PowerModList(a, 1/r, m)the -th roots of modulo , ascending

PowerModList(a, k, m)an integer exponent gives the single value

Domain: Hypercomplex algebra

Details

By CRT a root is a root in every channel independently, and an odd prime power has exactly the two square roots of 1, — so for ODD there are square roots of 1, one per sign vector across the places
counts DISTINCT primes; the 2-adic channel is the exception, with 1, 2 and 4 roots for , and
A square root of exists only where every odd prime factor is and — half the primes, so split units are generic and imaginary ones special
Square roots of take an exact CRT route with the root Hensel-lifted up each prime power, so is unbounded there; other roots are found by scanning and are capped
Sending for a split unit is a ring homomorphism, so the symbolic identities transport into

Examples