OFFSET
1,2
COMMENTS
Mordell shows that the only integer points on the elliptic curve y*(y+1) = x*(x+1)*(x+2) have x = -2, -1, 0, 1, 5, corresponding to the products 0, 6, 210. However, there are infinitely many rational points generated from (x,y) = (0,0) by the chord-and-tangent process. - Jonathan Sondow, Oct 12 2013
REFERENCES
Louis J. Mordell, Diophantine Equations, Academic Press 1969, p. 257.
FORMULA
Terms can be derived from the integral solutions to the elliptic curve y^2 = x^3 - 16*x + 16.
EXAMPLE
210 = 14*15 = 5*6*7.
MATHEMATICA
Module[{nn=20, p2, p3}, p2=Times@@@Partition[Range[0, nn], 2, 1]; p3= Times@@@ Partition[ Range[0, nn], 3, 1]; Intersection[p2, p3]] (* Harvey P. Dale, Oct 05 2019 *)
CROSSREFS
KEYWORD
fini,full,nonn,bref
AUTHOR
Andrew Niedermaier, Jul 16 2006
STATUS
approved