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7 - General Properties of Congruences

Table of contents

  • 7.1 Roots of Congruences
  • 7.2 Integral Polynomials and Identical Congruences
  • 7.3 Divisibility of Polynomials \pmod m
  • 7.4 Roots of Congruences to a Prime Modulus
  • 7.5 Some Applications of the General Theorems
  • 7.6 Lagrange’s Proof of Fermat’s and Wilson’s Theorems
  • 7.7 The Residue of (\frac{1}{2}(p - 1))!
  • 7.8 A Theorem of Wolstenholme
  • 7.9 The Theorem of Von Staudt
  • 7.10 Proof of Von Staudt’s Theorem

7.1 Roots of Congruences

7.2 Integral Polynomials and Identical Congruences

7.3 Divisibility of Polynomials (modm)

7.4 Roots of Congruences to a Prime Modulus

7.5 Some Applications of the General Theorems

7.6 Lagrange’s Proof of Fermat’s and Wilson’s Theorems

7.7 The Residue of (21​(p−1))!

7.8 A Theorem of Wolstenholme

7.9 The Theorem of Von Staudt

7.10 Proof of Von Staudt’s Theorem


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