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Journal Article

Improved Techniques for Lower Bounds for Odd Perfect Numbers

R. P. Brent, G. L. Cohen and H. J. J. Te Riele
Mathematics of Computation
Vol. 57, No. 196 (Oct., 1991), pp. 857-868
DOI: 10.2307/2938723
Stable URL: http://www.jstor.org/stable/2938723
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Improved Techniques for Lower Bounds for Odd Perfect Numbers
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Abstract

If N is an odd perfect number, and qk | N, q prime, k even, then it is almost immediate that $N > q^{2k}$. We prove here that, subject to certain conditions verifiable in polynomial time, in fact $N > q^{5k/2}$. Using this and related results, we are able to extend the computations in an earlier paper to show that $N > 10^{300}$.

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