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Powerpoint Templates

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  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.