Lower bounds for relatively prime amicable numbers of opposite parity.

Author:
Peter Hagis

Journal:
Math. Comp. **24** (1970), 963-968

MSC:
Primary 10.03

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 and are a pair of relatively prime amicable numbers of opposite parity then is greater than and and are each greater than .

**[1]**Peter Hagis Jr.,*On relatively prime odd amicable numbers*, Math. Comp.**23**(1969), 539–543. MR**0246816**, 10.1090/S0025-5718-1969-0246816-7**[2]**Peter Hagis Jr.,*Relatively prime amicable numbers of opposite parity*, Math. Mag.**43**(1970), 14–20. MR**0253977****[3]**Hans-Joachim Kanold,*Untere Schranken für teilerfremde befreundete Zahlen*, Arch. Math. (Basel)**4**(1953), 399–401 (German). MR**0058622****[4]**Hans Rademacher,*Lectures on elementary number theory*, A Blaisdell Book in the Pure and Applied Sciences, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR**0170844****[5]**Paul Bratley, Fred Lunnon, and John McKay,*Amicable numbers and their distribution*, Math. Comp.**24**(1970), 431–432. MR**0271005**, 10.1090/S0025-5718-1970-0271005-8

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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