492

From ProofWiki
Jump to navigation Jump to search

Previous  ... Next

Number

$492$ (four hundred and ninety-two) is:

$2^2 \times 3 \times 41$


The sum of $3$ cubes, either positive or negative, in $3$ known ways:
\(\ds \quad \ \ \) \(\ds 492\) \(=\) \(\ds 50^3 + \paren {-19}^3 + \paren {-49}^3\)
\(\ds \) \(=\) \(\ds 123 \, 134^3 + 9179^3 + \paren {-123 \, 151}^3\)
\(\ds \) \(=\) \(\ds 1 \, 793 \, 337 \, 644^3 + \paren {-813 \, 701 \, 167}^3 + \paren {-1 \, 735 \, 662 \, 109}^3\)


Its cube can be expressed as the sum of $3$ positive cubes in $13$ different ways:
\(\ds \quad \ \ \) \(\ds 492^3\) \(=\) \(\ds 24^3 + 204^3 + 480^3\)
\(\ds \) \(=\) \(\ds 48^3 + 85^3 + 491^3\)
\(\ds \) \(=\) \(\ds 72^3 + 384^3 + 396^3\)
\(\ds \) \(=\) \(\ds 113^3 + 264^3 + 463^3\)
\(\ds \) \(=\) \(\ds 114^3 + 360^3 + 414^3\)
\(\ds \) \(=\) \(\ds 149^3 + 336^3 + 427^3\)
\(\ds \) \(=\) \(\ds 176^3 + 204^3 + 472^3\)
\(\ds \) \(=\) \(\ds 190^3 + 279^3 + 449^3\)
\(\ds \) \(=\) \(\ds 207^3 + 297^3 + 438^3\)
\(\ds \) \(=\) \(\ds 226^3 + 332^3 + 414^3\)
\(\ds \) \(=\) \(\ds 243^3 + 358^3 + 389^3\)
\(\ds \) \(=\) \(\ds 246^3 + 328^3 + 410^3\)
\(\ds \) \(=\) \(\ds 281^3 + 322^3 + 399^3\)


Also see


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=492&oldid=479117"