Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T20:48:29.753Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Diophantine Equation x(x + d)(x + 2d) +y(y + d)(y + 2d) = z(z + d)(z + 2d)

Published online by Cambridge University Press:  20 November 2018

Leon Bernstein
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A previous result of the author concerning the parametric representation of infinitely many solutions of the title equation is strongly improved. New classes each containing infinitely many solutions of the equation for specified values of d are stated explicitly. The method of solution hinges heavily on solving the generalized Pell’s equation x2—Dy2=c.

Keywords

10 B10(Diophantine EquationsCubicQuartic Equations)
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 27 - 34
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bernstein, Leon, Explicit solutions of pyramidial diophantine equations, Canad. Math. Bull. Vol. 15(2) (1972), 177-184.Google Scholar
2. Bernstein, Leon, New infinite classes of periodic Jacobi-Perron algorithms. Pacific Jour. Math. Vol. 16, No. 3 (1966), 439-469.Google Scholar
3. Bernstein, Leon, The modified algorithm of Jacobi-Perron, Memoirs Amer. Math. Soc. No. 67 (1966), 1-44.Google Scholar
4. Oppenheim, A.,On the diophantine equation x3+y3+z3=x+y+z, Proc. Amer. Math. Soc. 16 (1965), 148-153.Google Scholar
5. Segal, S. L., A note on pyramidial numbers, Am. Math. Monthly (1962), 637-638.Google Scholar
6. Sierpinski, W., Sur une proprieté des nombres tétraedraux, Elemente Math. 7 (1962), 29-30.Google Scholar
7. Wunderlich, M.,Certain properties of pyramidial and figurate numbers, Math. Comp. 16 (1962), 482-486.Google Scholar