原根的存在性及个数证明(Primitive Root Theorem) 我在RSA学习总结的第三部分关于Mille-Rabin素数测试的正确性证明里需要用到此定理,由于证明太长,故另开一章于此。(为啥我说话突然文绉绉了Orz,可能是这周辩论打多了) 结论是对素数p,modulo p的原根存在,个数为与ø(p-1),modulo p2的原根个数为(p-1)ø(...
原根的存在性及个数证明（PrimitiveRootTheorem）我在RSA学习总结的第三部分关于Mille-Rabin素数测试的正确性证明⾥需要⽤到此定理，由于证明太长，故另开⼀章于此。（为啥我说话突然⽂绉绉了Orz，可能是这周辩论打多了）结论是对素数p，modulo p的原根存在，个数为与ø（p-1），modulo p2的原根个数为(p...
第十一节Wilson's Theorem 威尔逊定理 第十二节Pollard Rho's Method Pollard-Rho算法 第十三节Primitive Roots modulo p 模p原根 第十四节Primitive Roots modulo p^e 模p^e原根 第十五节Primitive Roots modulo n 模n原根 第十六节Quadratic Residues 二次剩余(包含Legendre Symbol 勒让德符号) 第十七节Legendre...
IMPLIMENTATION OF OPTIMUM ENCRYPTION ALGORITHM USING CHAOTIC SYSTEMS WITH THE APPLICATION OF PRIMITIVE ROOT THEOREMJATIN M PATELANUJ M PATEL
By Horie [4, Theorem 2], l [??] [h.sup.-.sub.n]/[h.sup.-.sub.n-1] for all n [greater than or equal to] 1 if l is a primitive root modulo [p.sup.2] and l is larger than an explicit but complicated constant depending on p. A note on the relative class number of the...
This theorem was proved by Gauss in 1801.Relation with the Euler function¶Let g be a primitive root modulo n . Then we can show that the smallest number k for which gk≡1(modn) is equal ϕ(n) . Moreover, the reverse is also...
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2) double-variable Shannon type sampling theorem 二元样本定理3) primitive root 本原元 1. The paper has proved the following generalized Golomb conjecture:if GF(q)is a finitc field and a,b,θ,are three nonzero elements,then there are two primitive roots x and y such that ax+by=θ ...
We make this explicit in Theorem 3 below. A Lehmer number which is also a primitive root modulo p will be called a Lehmer primitive root or an LPR. The inverse a¯ of an LPR is also an LPR. Since there is no Lehmer number modulo 3, we can suppose p>3. Wang and Wang [8] con...
Incidentally, a prime q such that 2q+1 is also a prime is known as a “Germain prime”. These were first studied by Sophie Germain in relation to the "first case" of Fermat’s Last Theorem. From Proposition 1 we see that every primitive exponential mapping corresponds to a Germain prime...