Interesting 9
Number Theory
Level
2
What is interesting about the number 9?
9 is the maximum number of perfect cubes required to sum to any integer
9 is the only perfect square that has 3 factors
9 is the only perfect power than is one less than another perfect power
9 is the number of Platonic solids
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1 solution
I do not know a formal proof but this is Waring's problem .
The max number of perfect cubes required to sum to any integer, g ( 3 ) = 9
Just to be clear on the other options:
• There are 5 platonic solids.
• 8 is the only perfect power one less than another perfect power.
• p 2 for all primes p has 3 factors: 1 , p , p 2 .