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A106321
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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.
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4
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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S. S. Gupta, 'Bhaskara Pairs' in 'Science Today' (subsequently renamed '2001') Jan 1988 pp. 68, Times of India, Mumbai.
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LINKS
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CROSSREFS
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KEYWORD
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hard,more,nonn,bref
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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