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 A195816 Edge lengths of Euler bricks. 6
 44, 85, 88, 117, 132, 140, 160, 170, 176, 187, 195, 220, 231, 234, 240, 252, 255, 264, 275, 280, 308, 320, 340, 351, 352, 374, 390, 396, 420, 425, 429, 440, 462, 468, 480, 484, 495, 504, 510, 528, 550, 560, 561, 572, 585, 595, 616, 640, 660, 680, 693, 700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Euler bricks are cuboids all of whose edges and face-diagonals are integers. REFERENCES L. E. Dickson, History of the Theory of Numbers, vol. 2, Diophantine Analysis, Dover, New York, 2005. P. Halcke, Deliciae Mathematicae; oder, Mathematisches sinnen-confect., N. Sauer, Hamburg, Germany, 1719, page 265. LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Euler brick FORMULA Integer edges a>b>c such that integer face-diagonals are d(a,b)=sqrt(a^2+b^2), d(a,c)=sqrt(a^2,c^2), d(b,c)=sqrt(b^2,c^2) EXAMPLE For n=1, the edges (a,b,c) are (240,117,44) and the diagonals (d(a,b),d(a,c),d(b,c)) are (267,244,125). MATHEMATICA ok[a_] := Catch[Block[{b, c, s}, s = Reduce[a^2 + b^2 == c^2 && b > 0 && c > 0, {b, c}, Integers]; If[s === False, Throw@ False, s = b /. List@ ToRules@ s]; Do[If[ IntegerQ@ Sqrt[s[[i]]^2 + s[[j]]^2], Throw@ True], {i, 2, Length@s}, {j, i - 1}]]; False]; Select[ Range[700], ok] (* Giovanni Resta, Nov 22 2018 *) CROSSREFS Cf. A031173, A031174, A031175. Sequence in context: A050272 A260201 A112721 * A118087 A335481 A345409 Adjacent sequences: A195813 A195814 A195815 * A195817 A195818 A195819 KEYWORD nonn AUTHOR Christopher Monckton of Brenchley, Oct 06 2011 STATUS approved

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Last modified September 15 11:09 EDT 2024. Contains 375938 sequences. (Running on oeis4.)