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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
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
Posted in Uncategorized
Tagged Consecutive Integers, Cubes, Sums of consecutive integers
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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
Posted in Number Puzzles
Tagged Cubes, Difference of cubes, Difference of squares, Squares
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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
Posted in Math Beauty, Number Puzzles
Tagged Consecutive Integers, Cubes, Squares, Sums
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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
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
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
Powers of Num3ers and their digits
A review of older posts Num3er N and N^2 use all digits 0-9 once Both 854 and 854^2 use all digits 1 to 9 854 854^2 = … Continue reading
Square and cube of 2-/3-digit num3ers that use different digits
Older post: Square and cube of 4-digit num3ers that use different digits 612^2 = 374544 612^3 = 229220928 543^2 = 294849 543^3 = 160103007 Can you find others? … Continue reading
