AoPS Number Theory Ch.13 Divisibility Rules

lilijia Post in AoPS_Number_Theory
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Congratulations to Jason, Julia, Alex, Susan, and Gioia on the Kahoot! Game today:)

Lesson review:

  • Let m be a nonnegative integer. Every nonnegative integer is congruent modulo 2^m, modulo 5^m, and modulo 10^m to its last m digits.
  • Every nonnegative integer is congruent modulo 3, modulo 9 to the sum of its digits.
  • Every nonnegative integer is congruent modulo 11 to the alternative sum of its digits.
  • 2n⇋units digit is even
  • 5n⇋units digit is 5 or 0
  • 10n⇋units digit is 0
  • k*2^m ⇋ its last m digits themselves form an integer that is a multiple of 2^m
  • k*5^m ⇋ its last m digits themselves form an integer that is a multiple of 5^m
  • k*10^m ⇋ its last m digits are all 0.
  • 3n⇋ the sum of its digit is 3k
  • 9n⇋ the sum of its digit is 9k
  • 11n⇋ the alternating sum of its digit is 11k

Extra Resource:

  • Divisibility rules for 2-12
  • Divisibility rule for 11
  • Divisibility rule for 9

Homework:

  • Pg. 252 Ex.13.2.1 (a,c), 13.2.2(c,f), 13.2.3(a,f), 13.2.4
  • Pg. 255 Ex.13.3.2, 13.3.4, 13.3.6
  • Pg. 257 Ex. 13.15 to 13.19, 13.25

No School next week. Enjoy the Memorial Day Holiday, and see you all on May 31st!

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