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

**[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)****[4]**H. Rademacher,*Lectures on Elementary Number Theory*, Blaisdell, Waltham, Mass., 1964. MR**30**#1079. MR**0170844 (30:1079)****[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