Category:Characterization of P-adic Unit has Square Root in P-adic Units
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This category contains pages concerning Characterization of P-adic Unit has Square Root in P-adic Units:
Let $\Z_p$ be the $p$-adic integers for some prime $p \ne 2$.
Let $Z_p^\times$ be the set of $p$-adic units.
Let $u \in Z_p^\times$ be a $p$-adic unit.
Let $u = c_0 + c_1p + c_2p^2 + \ldots$ be the $p$-adic expansion of $u$.
The following statements are equivalent::
- $(1)\quad \exists x \in \Z_p^\times : x^2 = u$
- $(2)\quad c_0$ is a quadratic residue of $p$
- $(3)\quad \exists y \in \Z_p : y^2 \equiv u \pmod{p\Z_p}$
Pages in category "Characterization of P-adic Unit has Square Root in P-adic Units"
The following 4 pages are in this category, out of 4 total.
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- Characterization of P-adic Unit has Square Root in P-adic Units
- Characterization of P-adic Unit has Square Root in P-adic Units/Condition 1 implies Condition 2
- Characterization of P-adic Unit has Square Root in P-adic Units/Condition 2 implies Condition 3
- Characterization of P-adic Unit has Square Root in P-adic Units/Condition 3 implies Condition 1