Non-elementary proper forcing

We introduce a simplified framework for ord-transitive models and Shelah's non elementary proper (nep) theory. We also introduce a new construction for the countable support nep iteration

On stronger conjectures that imply the Erd\"os-Moser conjecture

The Erd\"os-Moser conjecture states that the Diophantine equation $S_k(m) = m^k$, where $S_k(m)=1^k+2^k+...+(m-1)^k$, has no solution for positive integers $k$ and $m$ with $k \geq 2$. We show that stronger conjectures about consecutive values of the function $S_k$, that seem to be more naturally, imply the Erd\"os-Moser conjecture.Comment: 7 page

A conjecture about numerators of Bernoulli numbers related to Integer Sequence A092291

In this paper we disprove a conjecture about numerators of divided Bernoulli numbers $B_n/n$ and $B_n/n(n-1)$ which was suggested by Roland Bacher. We give some counterexamples. Finally, we extend the results to the general case.Comment: 11 page