1 / 13

321 Section, 2-7

321 Section, 2-7. Natalie Linnell. Prove or disprove that if a, b, c are positive integers and a|bc then a|b or a|c. How many zeros are there at the end of 100!. Prove that if n is an odd positive integer, then n 2  1 (mod 8). Use Fermat’s Little Theorem to compute 3 302 mod 5.

georgiae
Télécharger la présentation

321 Section, 2-7

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 321 Section, 2-7 Natalie Linnell

  2. Prove or disprove that if a, b, c are positive integers and a|bc then a|b or a|c

  3. How many zeros are there at the end of 100!

  4. Prove that if n is an odd positive integer, then n2 1 (mod 8)

  5. Use Fermat’s Little Theorem to compute 3302 mod 5

  6. Prove that if p is prime, and x2 = 1 (mod p) then x  1 (mod p) or x  (p-1) (mod p)

  7. Prove that if m and n are both perfect squares, then nm is a perfect square • What kind of proof did you do?

  8. Prove that if 3n+2 is odd, then n is odd • What kind of proof did you do?

  9. Show that the following is a tautology using a truth table • ((r→ (p v q)) → (p →(r →q))

  10. Let D(x,y) mean “team x defeated team y” and P(x,y) mean “team x has played team y” • Every team has lost at least one game. • There is a team that has beaten every team it has played.

  11. True or false: a  b (mod m), and b  c (mod m) implies that a2 bc (mod m)

  12. Is the argument correct? Why? • Every computer science major takes discrete mathematics. Natasha is taking discrete mathematics. Therefore, Natasha is a computer science major. • Everyone who eats granola every day is healthy. Linda is not healthy. Therefore, Linda does not eat granola every day.

  13. Show that ((p  q)  p)  qis a tautology using logical equivalences

More Related