1+2=3 (generalized) Math Club 3/19/2012 Powerpoint Templates
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.
Challenge 1 Show that 3 is a politenumber.
Challenge 2 Show that 9 is a politenumber.
Challenge 3 Is 4 a politenumber?
Challenge 4 Find all politenumbers.
Challenge 5 Show that all oddnumbers are polite.
Challenge 6 Show thatanynumber divisible by 3 ispolite.
Challenge 7 Provethatanynumber divisible by 7 ispolite.
Challenge 8 Let besomeoddnumber. Provethat for any, infinitelymany multiples of are polite. (in otherwords, above a certain point, all multiples of are polite)
Challenge 9 Challenge 8 istooweak. Let besomeoddnumber. Provethat for any, ALL multiples of are politenumbers.
Challenge 10 All numberswith an odd factor are polite. Whatnumbers are left?
Final Challenge (11) Show that a power of twocannotbepolite.