AoPS Number Theory: Ch. 14(II) Linear Congruences

lilijia Post in AoPS_Number_Theory
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Lesson review:

  • a linear congruence equation
  • an inverse: b*b^(-1) is congruent to 1 (mod m)
  • only if gcd (m,r)=1, otherwise r has no reverse modulo m.
  • if ak is congruent to bk (mod mk), then a is congruent to b (mod m)
  • if ac is congruent to bc (mod m), then a is congruent to b (mod m/gcd(m,c))
  • many remainder problems are just linear congruences.

Extra Resource

Homework

  • Pg. 270 Ex.14.3.1, 14.3.3, 
  • Pg. 275 Ex.14.4.1, 14.4.4, 14.4.5
  • Pg. 278 Ex. 14.20, 14.27, 14.29  to 14.31

Feel free to reach out if you have any questions in this Chapter. We will learn Ch.15 next Sunday, and have our final exam on 6/21.

Make sure you study hard and start your review as early as possible:)

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