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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 (list; graph; refs; listen; history; text; internal format)
 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 Adjacent sequences:  A334186 A334187 A334188 * A334190 A334191 A334192 KEYWORD nonn,full,fini,bref AUTHOR Bernard Schott, Apr 18 2020 STATUS approved

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Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)