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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_rings.html" title="">rings</a> > <a href="_integers_spmodulo_spa_spprime.html" title="">integers modulo a prime</a></div>
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<div><h1>integers modulo a prime</h1>
<div>Create the ring of integers modulo a prime number <tt>p</tt> as follows.<table class="examples"><tr><td><pre>i1 : R = ZZ/101
o1 = R
o1 : QuotientRing</pre>
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We can create elements of the ring as follows.<table class="examples"><tr><td><pre>i2 : 9_R
o2 = 9
o2 : R</pre>
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<tr><td><pre>i3 : 103_R
o3 = 2
o3 : R</pre>
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The usual arithmetic operations are available.<table class="examples"><tr><td><pre>i4 : 9_R * 11_R
o4 = -2
o4 : R</pre>
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<tr><td><pre>i5 : 9_R ^ 11
o5 = 49
o5 : R</pre>
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<tr><td><pre>i6 : 9_R * 11_R == -2_R
o6 = true</pre>
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Find the inverse of an integer modulo a prime as follows.<table class="examples"><tr><td><pre>i7 : 17_R^-1
o7 = 6
o7 : R</pre>
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To view this element as an element of <tt>ZZ</tt> use the <a href="_lift.html" title="lift to another ring">lift</a> command.<table class="examples"><tr><td><pre>i8 : lift (17_R^-1, ZZ)
o8 = 6</pre>
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