568 to 7

Since the number 7 is in the name of the blog (for some reason that I don’t remember), a limited amount of associated numerology seems appropriate, if only as a filler.

568 is the smallest positive integer whose seventh power is the sum of seven seventh powers.

$\displaystyle 568^7=525^7+439^7+430^7+413^7+266^7+258^7+127^7$

According to Wolfram MathWorld, it is not known whether the seventh power of a positive integer can be written as the sum of 3, 4, 5, or 6 seventh powers.

More numerology:

• The fouriest transform of 568 is in base seven: 568=14417
• The digit 7 is conspicuously missing from the digits of 568