

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.


1




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 chordandtangent process.  Jonathan Sondow, Oct 12 2013


REFERENCES

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


LINKS



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



STATUS

approved



