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A318522
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Decimal expansion of sqrt(28^(1/3)-27^(1/3)).
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1
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1, 9, 1, 2, 8, 2, 4, 4, 0, 0, 6, 0, 9, 2, 8, 0, 1, 6, 7, 5, 1, 2, 9, 5, 5, 0, 6, 4, 7, 8, 3, 3, 5, 0, 9, 8, 9, 7, 2, 3, 0, 7, 2, 0, 7, 2, 5, 4, 5, 7, 1, 9, 1, 0, 5, 5, 3, 7, 7, 1, 1, 5, 0, 8, 1, 2, 5, 0, 5, 0, 9, 2, 3, 3, 9, 3, 9, 5, 6, 1, 9, 5, 8, 0, 8
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OFFSET
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0,2
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COMMENTS
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Ramanujan's question 525 (ii), see Berndt and Rankin in References: Show how to find the square roots of surds of the form A^(1/3) + B^(1/3), and hence prove that sqrt(28^(1/3)-27^(1/3)) = (98^(1/3)-28^(1/3)-1)/3.
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REFERENCES
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B. C. Berndt and R. A. Rankin, Ramanujan: Essays and Surveys, American Mathematical Society, 2001, ISBN 0-8218-2624-7, page 221 (JIMS 6, page 39 and pages 191-192).
Srinivasa Ramanujan, Collected Papers, Chelsea, 1962, page 327, Question 525.
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LINKS
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EXAMPLE
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0.191282440060928016751295506478335098972307207254571910553771150812505...
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MAPLE
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MATHEMATICA
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RealDigits[Sqrt[28^(1/3) - 27^(1/3)], 10, 120][[1]] (* Amiram Eldar, Jun 27 2023 *)
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PROG
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(PARI) sqrt(28^(1/3)-27^(1/3))
(PARI) p(x)=x^3+x^2+5*x-1;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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