Smallest Integer which is Sum of 2 Cubes in 4 Ways
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Theorem
The smallest positive integer which can be expressed as the sum of $2$ cubes in $4$ different ways is:
\(\ds 42 \, 549 \, 416\) | \(=\) | \(\ds 348^3 + 74^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 282^3 + 272^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \left({-2662}\right)^3 + 2664^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \left({-475}\right)^3 + 531^3\) |
Proof
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Sources
- Apr. 1993: Joseph H. Silverman: Taxicabs and Sums of Two Cubes (Amer. Math. Monthly Vol. 100, no. 4: pp. 331 – 340) www.jstor.org/stable/2324954
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $42,549,416$