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A Computer-Assisted Investigation of Ramanujan Pairs

A Computer-Assisted Investigation of Ramanujan Pairs

Four new Ramanujan pairs $\{ {a_i}\}$, $\{ {b_j}\}$ are given along with the theorem that no such pairs exist with ${a_1} = 1$ and ${a_2} = s$ for any $s \geqslant 5$. All finite Ramanujan pairs are determined and their significance in bounding the local branching degree in the search …