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

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`%I #14 Oct 05 2019 11:53:02
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`%S 0,6,210
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`%N Complete list of numbers that can be represented both as a product of 2 consecutive integers and as a product of 3 consecutive integers.
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`%C 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
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`%D Louis J. Mordell, Diophantine Equations, Academic Press 1969, p. 257.
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`%F Terms can be derived from the integral solutions to the elliptic curve y^2 = x^3 - 16*x + 16.
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`%e 210 = 14*15 = 5*6*7.
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`%t 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 *)
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`%Y Intersection of A002378 and A007531.
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`%K fini,full,nonn,bref
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`%O 1,2
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`%A _Andrew Niedermaier_, Jul 16 2006
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