A number-theoretic approach to homotopy exponents of SU(n)

We use methods of combinatorial number theory to prove that, for each n≥2 and any prime p, some homotopy group πi(SU(n)) contains an element of order pn−1+ordp(⌊n/p⌋!), where ordp(m) denotes the largest integer α such that pα∣m.