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Mathematics of Computation

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A computer-assisted investigation of Ramanujan pairs

Authors: Richard Blecksmith, John Brillhart and Irving Gerst
Journal: Math. Comp. 46 (1986), 731-749
MSC: Primary 11P57
MathSciNet review: 829643
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Abstract: 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 tree for such pairs is discussed. The search techniques and programs that were used are also described. The parity of the coefficients in the power series is determined in two of the new identities. Partition interpretations of the six recent identities are also given.

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Keywords: Ramanujan pairs, computer search tree
Article copyright: © Copyright 1986 American Mathematical Society