A195816 - OEIS

%I #34 Nov 22 2018 08:06:55

%S 44,85,88,117,132,140,160,170,176,187,195,220,231,234,240,252,255,264,

%T 275,280,308,320,340,351,352,374,390,396,420,425,429,440,462,468,480,

%U 484,495,504,510,528,550,560,561,572,585,595,616,640,660,680,693,700

%N Edge lengths of Euler bricks.

%C Euler bricks are cuboids all of whose edges and face-diagonals are integers.

%D L. E. Dickson, History of the Theory of Numbers, vol. 2, Diophantine Analysis, Dover, New York, 2005.

%D P. Halcke, Deliciae Mathematicae; oder, Mathematisches sinnen-confect., N. Sauer, Hamburg, Germany, 1719, page 265.

%H Robert G. Wilson v, <a href="/A195816/b195816.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EulerBrick.html">Euler brick</a>

%F 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)

%e 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).

%t 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 *)

%Y Cf. A031173, A031174, A031175.

%K nonn

%O 1,1

%A _Christopher Monckton of Brenchley_, Oct 06 2011