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Math 135 Midterm Exam-AID Session PowerPoint Presentation
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Math 135 Midterm Exam-AID Session. Agenda. 2.3 Linear Diophantine Equations 2.5 Prime Numbers 3.1 Congruence 3.2 Tests for Divisibility 3.4 Modular Arithmetic 3.5 Linear Congruences. Agenda. 3.6 The Chinese Remainder Theorem 3.7 Euler Fermat Theorem

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Presentation Transcript
agenda
Agenda
  • 2.3 Linear Diophantine Equations
  • 2.5 Prime Numbers
  • 3.1 Congruence
  • 3.2 Tests for Divisibility
  • 3.4 Modular Arithmetic
  • 3.5 Linear Congruences
agenda1
Agenda
  • 3.6 The Chinese Remainder Theorem
  • 3.7 Euler Fermat Theorem
  • 7.1-7.4 An Introduction to Cryptography
  • 8.1-8.8 Complex Numbers
2 3 linear diophantine equations
2.3 Linear Diophantine Equations
  • Definition
    • Linear Diophantine Equation is an equation in one or more unknowns with integer coefficients, for which integer solutions are sought
  • Linear Diophantine Equation Theorem
2 5 prime numbers1
2.5 Prime Numbers
  • Proposition 2.51
  • Euclid Theorem 2.52
  • Theorem 2.52
  • Unique Factorization Theorem 2.54
2 5 prime numbers2
2.5 Prime Numbers
  • Theorem 2.55
  • Proposition 2.56
2 5 prime numbers3
2.5 Prime Numbers
  • Theorem 2.57
  • Theorem 2.58
2 5 prime numbers4
2.5 Prime Numbers
  • Example
  • Example
  • Example
3 1 congruence
3.1 Congruence
  • Definition
  • Proposition 3.11
3 2 tests for divisibility
3.2 Tests for Divisibility
  • Theorem 3.21
    • A number is divisible by 9 if and only if the sum of its digits is divisible by 9.
  • Theorem 3.22
    • A number is divisible by 3 if and only if the sum of its digits is divisible by 3.
  • Proposition 3.23
    • A number is divisible by 11 if and only if the alternating sum of its digits is divisible by 11.
3 4 modular arithmetic1
3.4 Modular Arithmetic
  • Fermat’s Little Theorem
  • Corollary 3.43
3 5 linear congruences
3.5 Linear Congruences
  • Definition
  • Linear Congruence Theorem 3.54
3 5 linear congruences1
3.5 Linear Congruences
  • Example
  • Example
  • Example
  • Example
proofs to memorize
Proofs to Memorize
  • Euclid’s Theorem 2.52
  • Proposition 2.53
  • Proposition 3.12
  • Proposition 3.14
  • Fermat’s Little Theorem 3.42
  • Proposition 7.41
  • Theorem 8.61
thanks
Thanks!

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