OFFSET
1,1
COMMENTS
Boyd and Kisilevsky in 1972 proved that there exist only 3 solutions (x,y) = (2,1), (4,2), (55,19) to the Diophantine equation x * (x+1) * (x+2) = y * (y+1) * (y+2) * (y+3) [see the reference and a proof in the link].
A similar result: in 1963, L. J. Mordell proved that (x,y) = (2,1), (14,5) are the only 2 solutions to the Diophantine equation x * (x+1) = y * (y+1) * (y+2) with 2*3 = 1*2*3 = 6 and 14*15 = 5*6*7 = 210.
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Revised edition), Penguin Books, 1997, entry 175560, p. 175.
LINKS
David. W. Boyd and Hershy Kisilevsky, The diophantine equation u(u+1)(u+2)(u+3) = v(v + 1)(v + 2), Pacific J. Math. 40 (1972), 23-32.
EXAMPLE
24 = 2*3*4 = 1*2*3*4;
120 = 4*5*6 = 2*3*4*5;
175560 = 55*56*57 = 19*20*21*22.
CROSSREFS
KEYWORD
nonn,full,fini,bref
AUTHOR
Bernard Schott, Apr 18 2020
STATUS
approved