MathDB

n-x balls in x+1 boxes

Source: Spanish MO 2012 Q3

June 7, 2012

combinatorics proposedcombinatorics

Problem Statement

Let

x

and

n

be integers such that

1\le x\le n

. We have

x+1

separate boxes and

n-x

identical balls. Define

f(n,x)

as the number of ways that the

n-x

balls can be distributed into the

x+1

boxes. Let

p

be a prime number. Find the integers

n

greater than

1

such that the prime number

p

is a divisor of

f(n,x)

for all

x\in\{1,2,\ldots ,n-1\}

.

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