Difference between revisions of "User:Temperal/The Problem Solver's Resource6"

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The Problem Solver's Resource

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Modulos

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Definition

$n\equiv a\pmod{b}$ if $n$ is the remainder when $a$ is divided by $b$ to give an integral amount.

Special Notation

Properties

For any number there will be only one congruent number modulo $m$ between $0$ and $m-1$ .

If $a\equiv b \pmod{m}$ and $c \equiv d \pmod{m}$ , then $(a+c) \equiv (b+d) \pmod {m}$ .

$a \pmod{m} + b \pmod{m} \equiv (a + b) \pmod{m}$ $a \pmod{m} - b \pmod{m} \equiv (a - b) \pmod{m}$ $a \pmod{m} \cdot b \pmod{m} \equiv (a \cdot b) \pmod{m}$

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 [[User:Temperal/The Problem Solver's Resource5|Back to page 5]] | [[User:Temperal/The Problem Solver's Resource7|Continue to page 7]]
 |}<br /><br />
+==Definition==
+*<math>n\equiv a\pmod{b}</math> if <math>n</math> is the remainder when <math>a</math> is divided by <math>b</math> to give an integral amount.
+==Special Notation==
+==Properties==
+For any number there will be only one congruent number modulo <math>m</math> between <math>0</math> and <math>m-1</math>.
+If <math>a\equiv b \pmod{m}</math> and <math>c \equiv d \pmod{m}</math>, then <math>(a+c) \equiv (b+d) \pmod {m}</math>.
+<math>a \pmod{m} + b \pmod{m} \equiv (a + b) \pmod{m}</math>
+<math>a \pmod{m} - b \pmod{m} \equiv (a - b) \pmod{m} </math>
+<math>a \pmod{m} \cdot b \pmod{m} \equiv (a \cdot b) \pmod{m} </math>
+<!-- to be continued -->

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