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Binomial and Floor Difference Crossed Division Determination (Posted on 2023-06-03) Difficulty: 3 of 5
Consider this function:
F(n, p) = nCp - ⌊n/p⌋
where n is a positive integer and p is a prime number.

Is F(n, p) always divisible by p?
If so, prove it.
If not, provide a counterexample.

Notes: nCp is the number of combinations of n elements taken p at a time. It is also known as Binomial Coefficient and read as "n choose p".
• ⌊m⌋ is equal to floor of m which is the greatest integer less than or equal to m

No Solution Yet Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): Computer solutionLarry2023-06-03 15:29:34
re: Computer solutionCharlie2023-06-03 12:07:38
SolutionComputer solutionLarry2023-06-03 08:33:34
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