{"schema":"vela.problem-packet.v0.1","problem":683,"statement":"Is it true that for every $1\\leq k\\leq n$ the largest prime divisor of $\\binom{n}{k}$, say $P(\\binom{n}{k})$, satisfies\\[P\\left(\\binom{n}{k}\\right)\\geq \\min(n-k+1, k^{1+c})\\]for some constant $c>0$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A006530","name":"Gpf(n): greatest prime dividing n, for n >= 2; a(1)=1.","terms":"1,2,3,2,5,3,7,2,3,5,11,3,13,7,5,2,17,3,19,5,7,11,23,3,5,13,3,7,29,5,31,2,11,17,7,3,37,19,13,5,41,7,43,11,5,23,47,3,7,5,1","url":"https://oeis.org/A006530"},{"id":"A074399","name":"a(n) is the largest prime divisor of n(n+1).","terms":"2,3,3,5,5,7,7,3,5,11,11,13,13,7,5,17,17,19,19,7,11,23,23,5,13,13,7,29,29,31,31,11,17,17,7,37,37,19,13,41,41,43,43,11,23,","url":"https://oeis.org/A074399"},{"id":"A121359","name":"Greatest prime factor of pyramidal number A000292(n).","terms":"2,5,5,7,7,7,5,11,11,13,13,13,7,17,17,19,19,19,11,23,23,23,13,13,13,29,29,31,31,31,17,17,17,37,37,37,19,41,41,43,43,43,23","url":"https://oeis.org/A121359"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}