For primes <mml:math alttext="$p \equiv 4$" id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≡</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>, <mml:math alttext="$11\left( {\bmod 15} \right)$" id="E6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>11</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>mod</mml:mo><mml:mn>15</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> explicit formulae are obtained for the cyclotomic numbers of order <mml:math alttext="$15$" id="E7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>15</mml:mn></mml:mrow></mml:math> over <mml:math alttext="${\text{GF}}\left( {p^2 } \right)$" id="E8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>GF</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>.

Cyclotomy of order <mml:math alttext="$15$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>15</mml:mn></mml:mrow></mml:math> over <mml:math alttext="${\text{GF}}\left( {p^2 } \right)$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>GF</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, <mml:math alttext="$p = 4$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>, <mml:math alttext="$11\left( {\bmod 15} \right)$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>11</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>mod</mml:mo><mml:mn>15</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>

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International Journal of Mathematics and Mathematical Sciences

Cyclotomy of order 15 over GF(p2), p=4, 11(mod15)

Abstract

Copyright