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We prove the polynomial analogues of some Liouville identities from elementary number theory. Consequently several sums defined over the finite fields are evaluated by combining the results obtained and some of the results from sums of reciprocals of polynomials over .

journal of applied mathematics

Evaluation of Some Sums of Polynomials in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">[</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">]</mml:mo></mml:math>

Evaluation of Some Sums of Polynomials in Fq[t]