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 A076440 n which appear to have a unique representation as the difference of two perfect powers and one of those powers is odd; that is, there is only one solution to Pillai's equation a^x - b^y = n, with a>0, b>0, x>1, y>1 and that solution has odd x or odd y (or both odd). 3
 1, 2, 10, 30, 38, 46, 122, 126, 138, 142, 146, 150, 154, 166, 170, 190, 194, 214, 222, 234, 270, 282, 298, 318, 338, 342, 354, 370, 382, 386, 406, 486, 490, 498, 502, 518, 546, 550, 566, 574, 582, 586, 594, 638, 666, 678, 686, 694, 710, 726, 730, 734, 746 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS There are two types of unique solutions. See A076438 for the general case. This sequence was found by examining all perfect powers (A001597) less than 2^63-1. By examining a larger set of perfect powers, we may discover that some of these numbers do not have a unique representation. REFERENCES R. K. Guy, Unsolved Problems in Number Theory, D9. T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986. LINKS M. E. Bennett, On Some Exponential Equations Of S. S. Pillai,Canad. J. Math. 53 (2001), 897-922. Eric Weisstein's World of Mathematics, Pillai's Conjecture CROSSREFS Cf. A001597, A076438, A076439. Sequence in context: A098425 A098408 A063564 * A047198 A290461 A162524 Adjacent sequences:  A076437 A076438 A076439 * A076441 A076442 A076443 KEYWORD hard,nonn AUTHOR T. D. Noe, Oct 12 2002 STATUS approved

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Last modified February 27 18:28 EST 2020. Contains 332307 sequences. (Running on oeis4.)