On multiple prime divisors of cyclotomic polynomials

Author:
Wayne L. McDaniel

Journal:
Math. Comp. **28** (1974), 847-850

MSC:
Primary 10A40; Secondary 10-04

DOI:
https://doi.org/10.1090/S0025-5718-1974-0387177-4

MathSciNet review:
0387177

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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. 213-222. 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. 149-150. 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. 417-418;*Collected Mathematical Papers*, v. 4, 1912, pp. 625-629.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0387177-4

Keywords:
Cyclotomic polynomial,
sum of divisors

Article copyright:
© Copyright 1974
American Mathematical Society