A120436 Complete list of numbers that can be represented both as a product of 2 consecutive integers and as a product of 3 consecutive integers.

0, 6, 210

Offset: 1

Author

Andrew Niedermaier, Jul 16 2006

Keywords

• fini
• full
• nonn
• bref

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

Examples

			210 = 14*15 = 5*6*7.
		

References

• Louis J. Mordell, Diophantine Equations, Academic Press 1969, p. 257.

Crossrefs

Intersection of A002378 and A007531.

Programs

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 *)

Formula

Terms can be derived from the integral solutions to the elliptic curve y^2 = x^3 - 16*x + 16.