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The purpose of this question is to resolve a mystery surrounding the prime 34511 that has got me bogged down for a while now. If you only care about the number theory and not the motivation coming ...

I seek a reference for the fact that "coefficients of the Hirzebruch $L$-polynomial have odd denominators". The coefficients are $$\frac{2^{2k}(2^{2k-1}-1)B_k}{(2k)!}$$ where $B_k$ is the Bernoulli ...