A rigorous method of finding biquadrate numbers whose sum is a biquadrate. (Q1509370)
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scientific article; zbMATH DE number 2662336
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A rigorous method of finding biquadrate numbers whose sum is a biquadrate. |
scientific article; zbMATH DE number 2662336 |
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A rigorous method of finding biquadrate numbers whose sum is a biquadrate. (English)
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1902
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Verf. gibt zunächst Lösungen der Aufgabe, 5 Biquadrate zu finden, deren Summe ein Biquadrat ist. Eine Reihe von Lösungen ist in der folgenden Identität enthalten: \[ \begin{multlined} (4m^2 -12n^2)^4 + (2m^2 -12mn -6n^2)^4 + (2m^2 + 12mn -6n^2)^4 \\ + (4m^2 + 12 n^2)^4 + (3m^2 +9n^2)^4 = (5m^2 + 15n^2)^4. \end{multlined} \] Alsdann gibt er Lösungen der analogen Aufgabe für 9 und 13 Biquadrate.
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Sums of fourth powers
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