2

Part of 2015 239 Open Mathematical Olympiad

Problems(1)

Writing a Binomial Coefficient as Product of $n$ Coprime Numbers

Source: 239 2015 P2

\binom{n+k}{n}

can be written as product of

n

pairwise coprime numbers

a_1,a_2,\dots,a_n

k+i

is divisible by

a_i

for all indices

i

number theorybinomial coefficients