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MCIII Number Theory 2.16

 
 
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Re: MCIII Number Theory 2.16
JinTina - 2024年01月14日 Sunday 09:43
 
Oh, is it because fractional(199/97)+fractional(199(96)/97) is equal to 1? I tried to prove it works for all k, but I need some help. Here is the algebraic proof:

{199*k/97}+{199*(97-k)/97}={199*k/97}+{199(-k)/97}={199*k/97}+{-(199*k/97)} and {x}+{-x}=1 so {199*k/97}+{-(199*k/97)}=1. But why is {x}+{-x}=1 true? 

Thanks,

Tina Jin

 
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