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Lower bounds for relatively prime amicable numbers of opposite parity.


Author: Peter Hagis
Journal: Math. Comp. 24 (1970), 963-968
MSC: Primary 10.03
DOI: https://doi.org/10.1090/S0025-5718-1970-0276167-4
MathSciNet review: 0276167
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Abstract: Whether or not a pair of relatively prime amicable numbers exists is an open question. In this paper it is proved that if $ m$ and $ n$ are a pair of relatively prime amicable numbers of opposite parity then $ mn$ is greater than $ {10^{121}}$ and $ m$ and $ n$ are each greater than $ {10^{60}}$.


References [Enhancements On Off] (What's this?)

  • [1] P. Hagis, Jr., "On relatively prime odd amicable numbers," Math. Comp., v. 23, 1969, pp. 539-543. MR 0246816 (40:85)
  • [2] P. Hagis, Jr., "Relatively prime amicable numbers of opposite parity," Math. Mag., v.43, 1970, pp. 14-20. MR 0253977 (40:7190)
  • [3] H.-J. Kanold, "Untere Schranken für teilerfremde befreundete Zahlen," Arch. Math., v. 4, 1953, pp. 399-401. MR 15, 400. MR 0058622 (15:400i)
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  • [5] P. Bratley, F. Lunnon & J. McKay, "Amicable numbers and their distribution," Math. Comp., v. 24, 1970, pp. 431-432. MR 0271005 (42:5888)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0276167-4
Keywords: Amicable numbers, relatively prime, opposite parity, lower bounds
Article copyright: © Copyright 1970 American Mathematical Society

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