E755 -- De casibus, quibus formulam x4 + mxxyy + y4 ad quadratum reducere licet
(On cases for which the formula x4 + mxxyy + y4 can be reduced to a square)
Summary:
Euler first dismisses the obvious cases when x = y and m = 2 or when one of the values is zero.
Then he goes on to solve the problem, finding about 90 values of m less than 200 for which solutions exist (section 13).
He closes with a "more elegant solution."
Publication:
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Originally published in Memoires de l'academie des sciences de St.-Petersbourg 7, 1820, pp. 10-22
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Opera Omnia: Series 1, Volume 5, pp. 35 - 47
- Reprinted in Commentat. arithm. 2, 1849, pp.492-500 [E755a]
Documents Available:
- Original publication: E755
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