Elementary bounds for Erdos problem 684
Let U(n,k) be the full prime-power part of the binomial coefficient n choose k supported on primes at most k. For all sufficiently large n, there exists k at most n with k at most 514(log n)^2 and U(n,k) greater than n squared. For arbitrarily large n greater than one, U(n,k) equals one throughout k at most (log n)/8. This independent Mathlib-only implementation adapts the known residue averaging and prime-power obstruction of APSSV26 with coarse Chebyshev constants. It does not formalize that paper's sharper coefficients or Bae's stronger registered lower bound. The optimal order remains…
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