On multiple prime divisors of cyclotomic polynomials
Author:
Wayne L. McDaniel
Journal:
Math. Comp. 28 (1974), 847850
MSC:
Primary 10A40; Secondary 1004
MathSciNet review:
0387177
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Abstract 
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Abstract: Let q be a prime and be the cyclotomic polynomial of order n. All triples (p, n, q) with p an odd prime when and when are given for which is divisible by .
 [1]
J. Brillhart, J. Tonascia & P. Weinberger, "On the Fermat quotient," Proceedings of the 1969 Atlas Symposium on Computers in Number Theory (Oxford, 1969), pp. 213222. MR 0314736 (47:3288)
 [2]
T. Nagell, Introduction to Number Theory, Wiley, New York, 1951. MR 13, 207. MR 0043111 (13:207b)
 [3]
H. Rademacher, Lectures on Elementary Number Theory, Blaisdell, Waltham, Mass., 1964. MR 30 #1079. MR 0170844 (30:1079)
 [4]
H. Riesel, "Note on the congruence ," Math. Comp., v. 18, 1964, pp. 149150. MR 28 #1156. MR 0157928 (28:1156)
 [5]
J. J. Sylvester, "On the divisors of the sum of a geometrical series whose first term is unity and common ratio any positive or negative number," Nature, v. 37, 1888, pp. 417418; Collected Mathematical Papers, v. 4, 1912, pp. 625629.
 [1]
 J. Brillhart, J. Tonascia & P. Weinberger, "On the Fermat quotient," Proceedings of the 1969 Atlas Symposium on Computers in Number Theory (Oxford, 1969), pp. 213222. MR 0314736 (47:3288)
 [2]
 T. Nagell, Introduction to Number Theory, Wiley, New York, 1951. MR 13, 207. MR 0043111 (13:207b)
 [3]
 H. Rademacher, Lectures on Elementary Number Theory, Blaisdell, Waltham, Mass., 1964. MR 30 #1079. MR 0170844 (30:1079)
 [4]
 H. Riesel, "Note on the congruence ," Math. Comp., v. 18, 1964, pp. 149150. MR 28 #1156. MR 0157928 (28:1156)
 [5]
 J. J. Sylvester, "On the divisors of the sum of a geometrical series whose first term is unity and common ratio any positive or negative number," Nature, v. 37, 1888, pp. 417418; Collected Mathematical Papers, v. 4, 1912, pp. 625629.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403871774
PII:
S 00255718(1974)03871774
Keywords:
Cyclotomic polynomial,
sum of divisors
Article copyright:
© Copyright 1974
American Mathematical Society
