%I #53 Aug 29 2017 03:21:25
%S 44,240,140,85,160,1008,187,429,832,780,828,1560,528,195,1155,1755,
%T 495,1575,2964,7840,2925,1008,4368,1080,10296,7579,8789,6072,14112,
%U 5643,4599,4900,6435,935,7920,7800,4928,7560,23760,1105,2163,2964
%N Shortest edge c of (measured by the longest edge) primitive Euler bricks (a, b, c, sqrt(a^2 + b^2), sqrt(b^2 + c^2), sqrt(a^2 + c^2) are integers).
%C Primitive means that gcd(a,b,c) = 1.
%C See A031173 for a list of the 3356 primitive bricks with c < b < a < 5*10^8. - _Giovanni Resta_, Mar 23 2014
%D Calculated by F. Helenius (fredh(AT)ix.netcom.com).
%H Giovanni Resta, <a href="/A031175/b031175.txt">Table of n, a(n) for n = 1..3556</a>
%H R. R. Gallyamov, I. R. Kadyrov, D. D. Kashelevskiy, <a href="https://arxiv.org/abs/1601.00636">A fast modulo primes algorithm for searching perfect cuboids and its implementation</a>, arXiv preprint arXiv:1601.00636 [math.NT], 2016.
%H A. A. Masharov and R. A. Sharipov, <a href="http://arxiv.org/abs/1504.07161">A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture</a>, arXiv preprint, 2015.
%H J. Ramsden and H. Sharipov, <a href="http://arxiv.org/abs/1207.6764">Inverse problems associated with perfect cuboids</a>, arXiv preprint arXiv:1207.6764, 2012. - From _N. J. A. Sloane_, Dec 23 2012
%H J. Ramsden and H. Sharipov, <a href="http://arxiv.org/abs/1208.1859">On singularities of the inverse problems associated with perfect cuboids</a>, arXiv preprint arXiv:1208.1859, 2012. - From _N. J. A. Sloane_, Dec 25 2012
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1108.5348">Perfect cuboids and irreducible polynomials</a>, arXiv:1108.5348, 2011
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1109.2534">A note on the first cuboid conjecture</a>, arXiv:1109.2534, 2011
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1201.1229">A note on the second cuboid conjecture. Part I</a>, arXiv:1201.1229, 2012
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1205.3135">Perfect cuboids and multisymmetric polynomials</a>, arXiv preprint arXiv:1205.3135, 2012. - From _N. J. A. Sloane_, Oct 22 2012
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1206.6769">On an ideal of multisymmetric polynomials associated with perfect cuboids</a>, arXiv preprint arXiv:1206.6769, 2012. - From _N. J. A. Sloane_, Dec 17 2012
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1207.2102">On the equivalence of cuboid equations and their factor equations</a>, arXiv preprint arXiv:1207.2102, 2012. - From _N. J. A. Sloane_, Dec 22 2012
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1207.4081">A biquadratic Diophantine equation associated with perfect cuboids</a>, arXiv preprint arXiv:1207.4081, 2012. - From _N. J. A. Sloane_, Dec 23 2012
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1208.0308">On a pair of cubic equations associated with perfect cuboids</a>, arXiv preprint arXiv:1208.0308, 2012. - From _N. J. A. Sloane_, Dec 23 2012
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1208.1227">On two elliptic curves associated with perfect cuboids</a>, arXiv preprint arXiv:1208.1227, 2012. - From _N. J. A. Sloane_, Dec 24 2012
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1505.02745">Asymptotic estimates for roots of the cuboid characteristic equation in the linear region</a>, arXiv preprint, 2015.
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1505.00724">Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture</a>, arXiv preprint, 2015.
%H Ruslan Sharipov, <a href="http://arxiv.org/abs/1507.01861">A note on invertible quadratic transformations of the real plane</a>, arXiv preprint arXiv:1507.01861, 2015
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EulerBrick.html">Euler Brick</a>
%H <a href="/index/Br#bricks">Index entries for sequences related to bricks</a>
%Y Cf. A031173, A031174.
%K nonn
%O 1,1
%A _Eric W. Weisstein_