y = C(n, 7) – floor(n/7)

 
 

Show that…

if   n \; > \; 7

then,

\dbinom{ \, n \, }{ \, 7 \, } \; - \; \lfloor n/7 \rfloor    is divisible by 7

 
 
 

floor \,(x) \; = \; \lfloor x \rfloor   is the largest integer not greater than   x   and
ceiling \,(x) \; = \; \lceil x \rceil   is the smallest integer not less than   x

C \, (n, r) \; = \; \dbinom{ \, n \, }{ \, r \, }   is the number of possible combinations of r objects from a set of n objects.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged , , . Bookmark the permalink.

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