2005
DOI: 10.1016/j.jnt.2004.07.009
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Rational tetrahedra with edges in arithmetic progression

Abstract: This paper discusses tetrahedra with rational edges forming an arithmetic progression, focussing specifically on whether they can have rational volume or rational face areas. Several infinite families are found which have rational volume, a face can have rational area only if its edges are themselves in arithmetic progression, and a tetrahedron can have at most one such rational face area.

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Cited by 3 publications
(9 citation statements)
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“…The discriminant of the curve is −2 4 3 12 23, so we can apply the 'Reduction mod p' map with p = 5. We find y 2 ≡ x 3 + 2 (mod 5) which has solutions (2, 0), (3,2), (3,3), (4, 1), (4,4). So |Ẽ(F 5 )| = 6 and since there are no points of order 2, E(Q) t ∼ = Z 3 .…”
Section: Gp Tetrahedra With Rational Volumementioning
confidence: 93%
See 4 more Smart Citations
“…The discriminant of the curve is −2 4 3 12 23, so we can apply the 'Reduction mod p' map with p = 5. We find y 2 ≡ x 3 + 2 (mod 5) which has solutions (2, 0), (3,2), (3,3), (4, 1), (4,4). So |Ẽ(F 5 )| = 6 and since there are no points of order 2, E(Q) t ∼ = Z 3 .…”
Section: Gp Tetrahedra With Rational Volumementioning
confidence: 93%
“…, there are two non-trivial rational points of order 3: (3,27) and (3, −27). The discriminant of the curve is −2 4 3 12 23, so we can apply the 'Reduction mod p' map with p = 5.…”
Section: Gp Tetrahedra With Rational Volumementioning
confidence: 99%
See 3 more Smart Citations