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Number 3 and its magic powers.
Does anybody know how the set of 1 3 9 27 81,... with two operations + and  can generate all integers, each member is used once. For example:32=27+931
 one year ago
 one year ago
Number 3 and its magic powers. Does anybody know how the set of 1 3 9 27 81,... with two operations + and  can generate all integers, each member is used once. For example:32=27+931
 one year ago
 one year ago

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mahmit2012Best ResponseYou've already chosen the best response.0
1=1 2=31 3=3 4=3+1 5=931 6=93 7=93+1 8=91 9=9 10=9+1 11=9+31 12=9+3 13=9+3+1 so we can make 113 with 1,3,9 14=2713 15=2712 16=2711 .... 28=27+1 29=27+2 ... 40=27+13 It shows we could make all 140 now 41=8140 42=8139 ..... 100=81+19 ... 121=81+40 then we can continue and proof by induction method.
 one year ago
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