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gcdmania
gcdmania
  • 61
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An upper bound for the G.C.D. of $binom$\binom{a}{3}$ and $binom$\binom{b}{3}$

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gcdmania
gcdmania
  • 61
  • 2

An upper bound for the G.C.D. of $binom{a}{3}$ and $binom{b}{3}$

I can't seem to find anything in the literature on how to estimate the g.c.d. of $\binom{a}{k}$ and $\binom{b}{k}$. In particular, I would like to know why $\gcd(\binom{a}{3}, \binom{b}{3})\leq b \binom{a-b}{3}$ for $a-b\geq 4$. I'm confident it's true (computer search).