Outline of a proof that every odd perfect number has at least eight prime factors
Author:
Peter Hagis
Journal:
Math. Comp. 35 (1980), 10271032
MSC:
Primary 10A20
MathSciNet review:
572873
Fulltext PDF Free Access
Abstract 
References 
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Abstract: An argument is outlined which demonstrates that every odd perfect number is divisible by at least eight distinct primes.
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E. Z. CHEIN, "Nonexistence of odd perfect numbers of the form and (Unpublished manuscript.)
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P. HAGIS, JR., "If n is odd and perfect then . A case study proof with a supplement in which the lower bound is improved to ." (Copy deposited in UMT file.)
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P. HAGIS, JR., "Every odd perfect number has at least eight prime factors." (Copy deposited in UMT file.)
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 E. Z. CHEIN, "Nonexistence of odd perfect numbers of the form and (Unpublished manuscript.)
 [2]
 P. HAGIS, JR., "If n is odd and perfect then . A case study proof with a supplement in which the lower bound is improved to ." (Copy deposited in UMT file.)
 [3]
 P. HAGIS, JR., "Every odd perfect number has at least eight prime factors." (Copy deposited in UMT file.)
 [4]
 P. HAGIS, JR. & W. L. McDANIEL, "On the largest prime divisor of an odd perfect number. II," Math. Comp., v. 29, 1975, pp. 922924. MR 0371804 (51:8021)
 [5]
 H. J. KANOLD, "Untersuchungen über ungerade volkommene Zahlen," J. Reine Angew. Math., v. 183, 1941, pp. 98109. MR 0006182 (3:268d)
 [6]
 W. L. McDANIEL, "On multiple prime divisors of cyclotomic polynomials," Math. Comp., v. 28, 1974, pp. 847850. MR 0387177 (52:8022)
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 T. NAGELL, Introduction to Number Theory, Wiley, New York, 1951. MR 0043111 (13:207b)
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 C. POMERANCE, "Odd perfect numbers are divisible by at least seven distinct primes," Acta. Arith., v. 25, 1974, pp. 265300. MR 0340169 (49:4925)
 [9]
 C. POMERANCE, "The second largest prime factor of an odd perfect number," Math. Comp., v. 29, 1975, pp. 914921. MR 0371801 (51:8018)
 [10]
 C. POMERANCE, "Multiply perfect numbers, Mersenne primes, and effective computability," Math. Ann., v. 226, 1977, pp. 195206. MR 0439730 (55:12616)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198005728739
PII:
S 00255718(1980)05728739
Article copyright:
© Copyright 1980
American Mathematical Society
