# Tag Archives: Cubes

## Concatenation | (x – y + z)^3 = x || y || z

Older post:   Concatenation: x||y||z = x^3 + y^3 + z^3   Find integers   x,   y   and   z   such that                                                  (x – y + z)^3   =   x || y || z                                                  … Continue reading

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## Sum of 7 consecutive num3ers is a cube

Older post:   Sum of 5 consecutive num3ers is a cube   Let   (x-3),   (x-2),   (x-1),   x,   (x+1),   (x+2),   (x+3)   be 7 consecutive integers. (x-3)   +   (x-2)   +   … Continue reading

## Num3ers such that a^2 – b^2 = x^3 and a^3 – b^3 = y^2

To find couples of integers   (a,   b)   such that                                                        a^2   –   b^2   =   x^3                                                        a^3   –   b^3   =   y^2 For example,     (10,   6) 10^2   … Continue reading

## Sum of 5 consecutive num3ers is a cube

Let   (x-2),   (x-1),   x,   (x+1),   (x+2)   be five consecutive integers. (x-2)   +   (x-1)   +   x   +   (x+1)   +   (x+2)   =   y^3 5*x   = … Continue reading

## Digits and Cubes

Find an integer with an odd number of odd digits only, which contains at least one each of the odd digits   1,   3,   5,   7,   9,   and whose cube also has an odd number … Continue reading

## Cubes | sum of their divisors are cubes

The factors of   81   are:     1     3     9     27     81 The prime factors are:     3 * 3 * 3 * 3   81   is the first square whose sum of its … Continue reading

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## Cubes Part 3 | sum of an n number of cubes in arithmetic progression

Arithmetic progression http://en.wikipedia.org/wiki/Arithmetic_progression http://mathworld.wolfram.com/ArithmeticProgression.html   The formula for finding the sum of an   n   number of cubes in arithmetic progression with common difference   d   and initial cube   a^3           (n/4)(2*a – d + d*n)(2*a^2 – … Continue reading

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## Cube Patterns| cubes of 1-99 — Part 1

1^3  =  1               99^3  =  970299 1 + 9 = 10           OR           1 + 99 = 100 2^3 = 8       … Continue reading