A note on diophantine equation

Author:
Josef Blass

Journal:
Math. Comp. **30** (1976), 638-640

MSC:
Primary 10B15

MathSciNet review:
0401638

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that if the class number of the quadratic field is not divisible by 5, and if *k* is not congruent to 7 modulo 8, then the equation has no solutions in rational integers *X*, *Y* with the exception of .

**[1]**A. I. Borevich and I. R. Shafarevich,*Number theory*, Translated from the Russian by Newcomb Greenleaf. Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. MR**0195803****[2]**J. H. E. Cohn,*Lucas and Fibonacci numbers and some Diophantine equations*, Proc. Glasgow Math. Assoc.**7**(1965), 24–28 (1965). MR**0177944****[3]**J. H. E. Cohn,*Eight Diophantine equations*, Proc. London Math. Soc. (3)**16**(1966), 153–166. MR**0190078****[4]**L. J. Mordell,*Diophantine equations*, Pure and Applied Mathematics, Vol. 30, Academic Press, London-New York, 1969. MR**0249355****[5]**O. WYLIE, "Solution of the problem: In the Fibonacci series , the first, second and twelfth terms are squares. Are there any others?,"*Amer. Math. Monthly,*v. 71, 1964, pp. 220-222.**[6]**J. Blass,*On the Diophantine equation 𝑌²+𝐾=𝑋⁵*, Bull. Amer. Math. Soc.**80**(1974), 329. MR**0330041**, 10.1090/S0002-9904-1974-13487-7

Retrieve articles in *Mathematics of Computation*
with MSC:
10B15

Retrieve articles in all journals with MSC: 10B15

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0401638-2

Article copyright:
© Copyright 1976
American Mathematical Society