Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2025-01-03T18:55:03.585Z Has data issue: false hasContentIssue false
  • English
  • Français

On Terai's conjecture concerning Pythagorean numbers

Published online by Cambridge University Press:  17 April 2009

Maohu A. Le
Maohu A. Le
Affiliation:
Department of Mathematics, Zhanjiang Normal College, Postal Code 524048, Zhanjiang, Guangdong, People's Republic of China
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.

In this paper we prove that if a, b, c, r are fixed positive integers satisfying a2 + b2 = cr, gcd(a, b) = 1, a ≡ 3(mod 8), 2 | b, r > 1, 2 ∤ r, and c is a (x,y,z) = (2, 2,r) satisfying x > 1, y > 1 and z > 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 329 - 334
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Laurent, M., Mignotte, M., and Nesterenko, Y., ‘Formes linéaries en deux logarithmes et déterminants d'interpolation’, J. Number Theory 55 (1995), 285–321.CrossRefGoogle Scholar
[2]Le, M.-H., ‘A note on the generalized Ramanujan-Nagell equation’, J. Number Theory 50 (1995), 193–201.CrossRefGoogle Scholar
[3]Le, M.-H., ‘A note on the diophantine equation (m 3 − 3m)x + (3m 2 − 1)y = (m 2 + 1)z’, Proc. Japan Acad. Ser. A Math. Sci 73 (1997), 148–149.Google Scholar
[4]Mordell, L.J., Diophantine equations (Academic Press, New York, 1969).Google Scholar
[5]Terai, N., ‘The diophantine equation ax + by = cz’, Proc. Japan Acad. Ser. A. Math. Sci 70 (1994), 22–26.Google Scholar
[6]Terai, N., ‘The diophantine equation ax + by = cz II’, Proc. Japan Acad. Ser. A. Math. Sci 71 (1995), 109–110.CrossRefGoogle Scholar
[7]Terai, N., ‘The diophantine equation ax + by = cz III’, Proc. Japan Acad. Ser. A. Math. Sci 72 (1996), 20–22.CrossRefGoogle Scholar
[8]Terai, N., ‘Applications of a lower bound for linear forms in two logarithms to exponential diophantine equations’ (to appear).Google Scholar