Modular Arithmetic
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Home > Art, Film & Photography > Modular Arithmetic: Euler's Totient Function, Fermat's Little Theorem, Chinese Remainder Theorem, Euler's Theorem, Carmichael Number
Modular Arithmetic: Euler's Totient Function, Fermat's Little Theorem, Chinese Remainder Theorem, Euler's Theorem, Carmichael Number

Modular Arithmetic: Euler's Totient Function, Fermat's Little Theorem, Chinese Remainder Theorem, Euler's Theorem, Carmichael Number


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 73. Chapters: Euler's totient function, Fermat's little theorem, Chinese remainder theorem, Euler's theorem, Carmichael number, Linear congruence theorem, Congruence relation, Proofs of Fermat's little theorem, Linear congruential generator, Quadratic reciprocity, Legendre symbol, Fermat primality test, Euler's criterion, Jacobi symbol, Quadratic residue, Quartic reciprocity, Cubic reciprocity, Primitive root modulo n, Gauss's lemma, Multiplicative group of integers modulo n, Verhoeff algorithm, Cipolla's algorithm, Montgomery reduction, Modular exponentiation, Root of unity modulo n, Tonelli-Shanks algorithm, Wilson's theorem, Solovay-Strassen primality test, Zeller's congruence, Luhn algorithm, Luhn mod N algorithm, Hensel's lemma, Carmichael function, Discrete logarithm, Kochanski multiplication, Pocklington's algorithm, Discrete logarithm records, Residue number system, Lehmer random number generator, Modular multiplicative inverse, Additive polynomial, Beaver bit-vector decision procedure, Mod n cryptanalysis, Multiplicative order, Vedic square, Congruence of squares, Method of successive substitution, Kronecker symbol, Reduced residue system, Jordan's totient function, Barrett reduction, Vantieghems theorem. Excerpt: In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic which gives conditions for the solvability of quadratic equations modulo prime numbers. There are a number of equivalent statements of the theorem, which consists of two "supplements" and the reciprocity law: Let p, q > 2 be two distinct (positive odd) prime numbers. Then (Supplement 1) x 1 (mod p) is solvable if and only if p 1 (mod 4).(Supplement 2) x 2 (mod p) is solvable if and only if p 1 (mod 8).(Quadratic reciprocity)Let q = q where the sign is plus if q 1 (mod 4) and minus if q 1 (mod 4). (I.e. -q...


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Product Details
  • ISBN-13: 9781156479278
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 74
  • Spine Width: 4 mm
  • Weight: 150 gr
  • ISBN-10: 1156479274
  • Publisher Date: 29 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Euler's Totient Function, Fermat's Little Theorem, Chinese Remainder Theorem, Euler's Theorem, Carmichael Number
  • Width: 189 mm


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