Nair's and Farhi's identities involving the least common multiple of binomial coefficients are equivalent

Details Nair's and Farhi's identities involving the least common multiple of binomial coefficients are equivalent Nair's and Farhi's identities involving the least common multiple of binomial coefficients are equivalent

2009-07-20

arxiv.org/abs/0907.3401v1

Mathematics

Number Theory

3 pages

Scientific paper

In 1982, Nair proved the identity: ${\rm lcm}({k \choose 1}, 2{k \choose 2}, >..., k{k \choose k}) ={\rm lcm}(1, 2, ..., k), \forall k\in \mathbb{N}.$ Recently, Farhi proved a new identity: ${\rm lcm}({k \choose 0}, {k \choose 1}, >..., {k \choose k}) =\frac{{\rm lcm}(1, 2, ..., k+1)}{k+1}, \forall k\in \mathbb{N}.$ In this note, we show that Nair's and Farhi's identities are equivalent.

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