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.
2
10
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
an integer
The product would be a positive integer.
2
x = 484
45
10
5
The only solution is that a = 5 then 25a = 25 x 5 = 52 x 5 = 53.
It is the additive inverse of itself, it is the square, cube, ... any positive power of itself.
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
Here is a method: cube root of 400g = n, where n is an integer cube both sides: 400g = n3 then: g = n3/400 therefore: n3/400 must be an integer if this is so, then n3 must be divisible by 400 with no remainder, and n must be => cube root of 400 which is 7.368 bracket the answer by substitution: let n=8, n cubed = 512 no good let n=12, n cubed = 1728 no good let n=20, n cubed = 8000, 8000/400=20 OK No smaller value of n will be divisible by 400 without a remainder, so g=20 is the smallest positive integer that meets the requirement.
an integer
The absoluate value of a positive integer is the integer itself.The absoluate value of a positive integer is the integer itself.The absoluate value of a positive integer is the integer itself.The absoluate value of a positive integer is the integer itself.
The product would be a positive integer.