3.39. Recall that for any a E F;, the discrete logarithm of a (with respect to aprimitive root g) is a number log,(a) satisfyingglogg(a) = a (mod p).Prove that(-1)l0%,(a)for all a E F;.Thus quadratic reciprocity gives a fast method to compute the parity of log, (a).

Name: 3.39. Recall that for any a E F;, the discrete logarithm of a (with r
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Description: 3.39. Recall that for any a E F;, the discrete logarithm of a (with respect to aprimitive root g) is a number log,(a) satisfyingglogg(a) = a (mod p).Prove that(-1)l0%,(a)for all a E F;.Thus quadratic reciprocity gives a fast method to compute the pa

Given that, The discrete logarithm of a is a number logga satisfying, glogga≡a mod p A number g is a…

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3.39. Recall that for any a e F;, the discrete logarithm of a (with respect to a primitive root g) is a number log, (a) satisfying glosg(a) = a (mod p). Prove that =(-1)lo8,(a) for all a E F;. Thus quadratic reciprocity gives a fast method to compute the parity of log, (a).

3.39. Recall that for any a e F;, the discrete logarithm of a (with respect to a primitive root g) is a number log, (a) satisfying glosg(a) = a (mod p). Prove that =(-1)lo8,(a) for all a E F;. Thus quadratic reciprocity gives a fast method to compute the parity of log, (a).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 27E

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