Powerpoint Templates

# Powerpoint Templates

## Powerpoint Templates

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

1. 1+2=3 (generalized) Math Club 3/19/2012 Powerpoint Templates

2. Definition Weshould all know that 1+2=3. A politenumberis a numberthatcanbewritten as a sum of positive consecutivenumbers. For example, 4+5+6+7 is 22, so 22 is a politenumber. Through a few challenges, wewill know everythingthereis to know about politenumbers by the end of thispowerpoint.

3. Challenge 1 Show that 3 is a politenumber.

4. Challenge 2 Show that 9 is a politenumber.

5. Challenge 3 Is 4 a politenumber?

6. Challenge 4 Find all politenumbers.

7. Challenge 5 Show that all oddnumbers are polite.

8. Challenge 6 Show thatanynumber divisible by 3 ispolite.

9. Challenge 7 Provethatanynumber divisible by 7 ispolite.

10. Challenge 8 Let besomeoddnumber. Provethat for any, infinitelymany multiples of are polite. (in otherwords, above a certain point, all multiples of are polite)

11. Challenge 9 Challenge 8 istooweak. Let besomeoddnumber. Provethat for any, ALL multiples of are politenumbers.

12. Challenge 10 All numberswith an odd factor are polite. Whatnumbers are left?

13. Final Challenge (11) Show that a power of twocannotbepolite.