Is gcd(a, b) * C(b,a)/b always an integer?

 
 
gcd \, (\, 2, \,  3 \, ) \; \times \; \dbinom{\, 3 \,}{\, 2 \,}\, /\, 3 \; = \; 1

gcd \, ( \, 2, \, 8 \, ) \; \times \; \dbinom{\, 8\, }{\, 2\, }\, /\, 8 \; = \; 7

gcd \, ( \, 2, \, 9 \, ) \; \times \;  \dbinom{\, 9\, }{\, 2\, }\, /\, 9 \; = \; 4

gcd \, ( \, 4, \, 6 \, ) \; \times \; \dbinom{\, 6\, }{\, 4\, }\, /\, 6  \; = \; 5

 

Is   gcd \,(\, a, \, b \,) \; \times \;  \dbinom{\, b\, }{\, a\, }\, /\, b   always an integer for every pair (a, b)   of postive integers
with   1 \leq a \leq b

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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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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