0
A positive integer n cubed always can be represented as the sum of consecutive odd numbers. Yet finding this decomposition can seem difficult, as is apparent from considering examples, e.g., "find 'cubes as odds' representations for 125 = 53, 343 = 73, or 117,649 = 3433." We give a descriptive method for this process and a formula with proof by mathematical induction.
Still curious? Ask our experts.
Chat with our AI personalities
Vivi
Professor
JordanAdd your answer:
Earn +20 pts
What is the least positive integer x for which 12x is the cube of an integer?
2
What is the least positive integer n such that the product 800n is a perfect cube?
10
What is the difference between a cube and a perfect cube?
A cube is any number multiplied by itself three times, eg 2 cubed = 2³ = 2×2×2 = 8; 1.5³ = 1.5×1.5×1.5 = 3.375 A perfect cube is an integer (whole number) that is the cube of an integer, eg 8 is a perfect cube as it is 2 cubed, but 9 is not a perfect cube as 9 = 2.08008382...³
The square root of a perfect square and the cube root of a perfect cube is?
an integer
What is the product of a positive integer and a positive integer?
The product would be a positive integer.
