Some computational results on a problem concerning powerful numbers

Mathematics of Computation

Volumn 50, Issue 182, 1988, Pages 619-632

  Stephens, A J ^a   Williams, H C ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966230943     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1988-0929558-3     Document Type: Article

References (15)

1. N. C. ANKENY, E. ARTIN & S. CHOWLA, “The class number of real quadratic number fields, ” Ann. of Math., v. 56, 1952, pp. 479-493.
2. B. D. BEACH, H. C. Williams & C. R. ZARNKE, Some Computer Results on Units in Quadratic and Cubic Fields, Proc. 25th Summer Meeting Canad. Math. Congr., Lakehead Univ., 1971, pp. 609-648.
3. G. CHRYSTAL, Textbook of Algebra, part 2, 2nd ed., Dover reprint, New York, 1969, pp. 423-490.
4. P. ERDOS, “Consecutive numbers, ” Eureka 38, 1975-1976, pp. 3-8.
5. A. GRANVILLE, “Powerful numbers and Fermat’s Last Theorem, ” C. R. Math. Rep. Acad. Sci. Canada, v. 8, 1986, pp. 215-218.
6. H. W. LENSTRA, JR., On the Calculation of Regulators and Class Numbers of Quadratic Fields, London Math. Soc. Lecture Note Series, vol. 56, 1982, pp. 123-150.
7. R. A. MOLLIN & P. G. WALSH, “A note on powerful numbers, quadratic fields, and the Pellian, ” C. R. Math. Rep. Acad. Sci. Canada, v. 8, 1986, pp. 109-111.
8. L. J. MORDELL, “On a Pellian equation conjecture, ” Acta Arith., v. 6, 1960, pp. 137-144.
9. OSKAR PERRON, Die Lehre von den Kettenbriichen, 2nd ed., Chelsea, New York, 1950.
10. R. J. SCHOOF, “Quadratic fields and factorization, ” Computational Methods in Number Theory (H. W. Lenstra, Jr. and R. Tijdemann, eds.), Math. Centrum Tracts, Number 155, Part II, Amsterdam, 1983, pp. 235-286.
11. D. SHANKS, Class Number, A Theory of Factorization and Genera, Proc. Sympos. Pure Math., vol. 20 (1969 Institute on Number Theory), Amer. Math. Soc., Providence, R. I., 1971, pp. 415
12. D. SHANKS, The Infrastructure of a Real Quadratic Field and Its Applications, Proc. 1972 Number Theory Conference, Boulder, 1972, pp. 217-224.
13. R. SOLENG, “A computer investigation of units in quadratic number fields, ” unpublished manuscript.
14. H. C. WILLIAMS, “A numerical investigation into the length of the period of the continued fraction expansion of √D, ” Math. Comp., v. 34, 1981, pp. 593-601.
15. H. C. WILLIAMS & M. C. WUNDERLICH, “On the parallel generation of the residues for the continued fraction factoring algorithm, ” Math. Comp., v. 48, 1987, pp. 405-423.