A031175 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).

44, 240, 140, 85, 160, 1008, 187, 429, 832, 780, 828, 1560, 528, 195, 1155, 1755, 495, 1575, 2964, 7840, 2925, 1008, 4368, 1080, 10296, 7579, 8789, 6072, 14112, 5643, 4599, 4900, 6435, 935, 7920, 7800, 4928, 7560, 23760, 1105, 2163, 2964

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Primitive means that gcd(a,b,c) = 1.

See A031173 for a list of the 3356 primitive bricks with c < b < a < 5*10^8. - Giovanni Resta, Mar 23 2014

References

• Calculated by F. Helenius (fredh(AT)ix.netcom.com).

Links

• Giovanni Resta, Table of n, a(n) for n = 1..3556
• R. R. Gallyamov, I. R. Kadyrov, D. D. Kashelevskiy, A fast modulo primes algorithm for searching perfect cuboids and its implementation, arXiv preprint arXiv:1601.00636 [math.NT], 2016.
• A. A. Masharov and R. A. Sharipov, A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture, arXiv preprint, 2015.
• J. Ramsden and H. Sharipov, Inverse problems associated with perfect cuboids, arXiv preprint arXiv:1207.6764, 2012. - From _N. J. A. Sloane_, Dec 23 2012
• J. Ramsden and H. Sharipov, On singularities of the inverse problems associated with perfect cuboids, arXiv preprint arXiv:1208.1859, 2012. - From _N. J. A. Sloane_, Dec 25 2012
• Ruslan Sharipov, Perfect cuboids and irreducible polynomials, arXiv:1108.5348, 2011
• Ruslan Sharipov, A note on the first cuboid conjecture, arXiv:1109.2534, 2011
• Ruslan Sharipov, A note on the second cuboid conjecture. Part I, arXiv:1201.1229, 2012
• Ruslan Sharipov, Perfect cuboids and multisymmetric polynomials, arXiv preprint arXiv:1205.3135, 2012. - From _N. J. A. Sloane_, Oct 22 2012
• Ruslan Sharipov, On an ideal of multisymmetric polynomials associated with perfect cuboids, arXiv preprint arXiv:1206.6769, 2012. - From _N. J. A. Sloane_, Dec 17 2012
• Ruslan Sharipov, On the equivalence of cuboid equations and their factor equations, arXiv preprint arXiv:1207.2102, 2012. - From _N. J. A. Sloane_, Dec 22 2012
• Ruslan Sharipov, A biquadratic Diophantine equation associated with perfect cuboids, arXiv preprint arXiv:1207.4081, 2012. - From _N. J. A. Sloane_, Dec 23 2012
• Ruslan Sharipov, On a pair of cubic equations associated with perfect cuboids, arXiv preprint arXiv:1208.0308, 2012. - From _N. J. A. Sloane_, Dec 23 2012
• Ruslan Sharipov, On two elliptic curves associated with perfect cuboids, arXiv preprint arXiv:1208.1227, 2012. - From _N. J. A. Sloane_, Dec 24 2012
• Ruslan Sharipov, Asymptotic estimates for roots of the cuboid characteristic equation in the linear region, arXiv preprint, 2015.
• Ruslan Sharipov, Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture, arXiv preprint, 2015.
• Ruslan Sharipov, A note on invertible quadratic transformations of the real plane, arXiv preprint arXiv:1507.01861, 2015
• Eric Weisstein's World of Mathematics, Euler Brick
• Index entries for sequences related to bricks

Crossrefs

Cf. A031173, A031174.