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• ## Re: prime, prime square, prime cube

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• ... I not have read either of those. I have, however, read L. J. Mordell, On the Integer Solutions of the Equation, e*y^2 = a*x^3+b*x^2+c*x+d, Proc. London
Feb 28, 2012 1 of 9
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"WarrenS" <warren.wds@...> wrote:

> > The actual history is both more complex and more
> > interesting than Warren's mistaken attribution.
>
> I have reason to believe, but unconfirmed since I do not
> have access to these papers, that one or both of the
> following papers by Mordell do do the job:
> Cambridge Philos Soc Proc 21(1922) 179-192.
> Quart J Pure Appl Math 45 (1914) 170-186.

L. J. Mordell,
On the Integer Solutions of the Equation,
e*y^2 = a*x^3+b*x^2+c*x+d,
Proc. London Math. Soc. s2-21(1) (1923) 415-419
doi:10.1112/plms/s2-21.1.415

where Mordell concedes that this problem
was solved by Thue in 1909, with a result very
different from Mordell's false claim of 1913.

In Cassel's obituary of Mordell:

Louis Joel Mordell, 1888-1972,
by J. W. S. Cassels, in
Biographical Memoirs of Fellows of the Royal Society,
Vol. 19 (Dec., 1973), pp. 493-520.

there is mention of an earlier retraction, circa 1919-1920:

>> In a paper which was little noticed at the time Thue
finitely many integral solutions for any cubic form
(or more generally, for any other than a power of a
he would have deduced at once that y^2 = x^3+ k has
only finitely many integral solutions x,y; at least with
x prime to 2k. As a matter of fact he only learned
of Thue's result later (paper 15) and at the time
he believed that there could be infinitely many solutions
for some k (cf. end of paper 2).<<

"Paper 15" seems to be:

L J Mordell,
A statement by Fermat,
Proc. Lond. Math. Soc., (2) 18 (1920) v.

The index for that volume indicates that this paper
was read in 1919, but not printed in the journal.
So 1919 is the earliest date for a retraction, by Mordell,
of his false claim of 1913, that I seen cited.

David
• ... Unless there just happens to be one or more of the form 5, x^2 = 5 + k, y^3 = 5 + 2k Kermit
Mar 4, 2012 1 of 9
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> Note that the difference can't be ±1 (mod 5).

> Best regards,

> Andrey

Unless there just happens to be one or more of the form

5, x^2 = 5 + k, y^3 = 5 + 2k

Kermit
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