Category:Congruence Modulo Equivalence for Integers in P-adic Integers
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This category contains pages concerning Congruence Modulo Equivalence for Integers in P-adic Integers:
Let $\Z_p$ be the $p$-adic integers for some prime $p$.
For any $a, b \in \Z_p$ and $n \in \N$, let $x \equiv y \pmod{p^n \Z_p}$ denote congruence modulo the principal ideal $p^n\Z_p$.
For any integers $a, b \in \Z$ and $n \in \N$, let $x \equiv y \pmod{p^n}$ denote congruence modulo integer $p^n$.
Let $x, y \in \Z$ be integers.
Let $k \in \N_{>0}$.
The following statements are equivalent:
- $(1)\quad x \equiv y \pmod{p^k \Z_p}$
- $(2)\quad x \equiv y \pmod{p^k}$
- $(3)\quad p^k \divides \paren{x - y}$
Pages in category "Congruence Modulo Equivalence for Integers in P-adic Integers"
The following 2 pages are in this category, out of 2 total.