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A334189
Positive solutions m of the Diophantine equation x * (x+1) * (x+2) = y * (y+1) * (y+2) * (y+3) = m.
0
24, 120, 175560
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
Cf. A121234.
Sequence in context: A052581 A052605 A195917 * A042120 A002980 A244794
KEYWORD
nonn,full,fini,bref
AUTHOR
Bernard Schott, Apr 18 2020
STATUS
approved