A106321 Smaller member of a Bhaskara pair (excluding Bhaskara twins, that is, include only a < b); a Bhaskara pair (a,b) is such that a^2 + b^2 = X^3 and a^3 + b^3 = Y^2.

625, 40000, 455625

Offset: 1

Author

Lekraj Beedassy, Apr 29 2005

Keywords

• hard
• more
• nonn
• bref

Comments

Ordered by the larger of the pair. For corresponding larger value see A106322.

The sequence is infinite because it contains (as a subsequence) all numbers of the form a = 625*s^6 where s is a positive integer. The pairs are (a,b=2*a) =(625*s^6, 1250*s^6) associated with (X,Y) = (125*s^4, 46875*s^9). - R. J. Mathar, Jan 26 2017

The sequence also contains all numbers of the form a = 3430000*s^6 where s is a positive integer. The pairs are (a,b=3*a) associated with (X,Y) = (49000*s^4, 33614000000*s^9). The sequence also contains all numbers of the form a = 22936954625 *s^6 with b=4*a, all numbers of the form a = 19592846 *s^6 with b=5*a, all numbers of the form a = 19150763710393 *s^6 with b=6*a, all numbers of the form a= 3975350 *s^6 with b=7*a, all numbers of the form a = 3305810795625 * s^6 with b=8*a. - R. J. Mathar, Jan 26 2017

References

• S. S. Gupta, 'Bhaskara Pairs' in 'Science Today' (subsequently renamed '2001') Jan 1988 pp. 68, Times of India, Mumbai.

Crossrefs

Cf. A106322, A106318, A106319, A106320.

Extensions

Corrected and extended Jud McCranie, Jul 04 2013