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Perfect magic cube. In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars, and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant. [1][2][3] Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist, [4] and cubes ...
Perfect number. In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
Cube (algebra) y = x3 for values of 1 ≤ x ≤ 25. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3. The cube is also the number ...
The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p. As of 2023, there are 51 known Mersenne primes (and therefore perfect numbers), the largest 17 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search, or GIMPS. [2]
The six classes. Simple: The minimum requirements for a magic cube are: all rows, columns, pillars, and 4 space diagonals must sum to the same value. A simple magic cube contains no magic squares or not enough to qualify for the next class. The smallest normal simple magic cube is order 3. Minimum correct summations required = 3 m2 + 4. Diagonal:
Euler brick. In mathematics, an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found.
John R. Hendricks. John Robert Hendricks (September 4, 1929 – July 7, 2007) was a Canadian amateur mathematician notable for his work in magic squares and hypercubes. He published many articles in the Journal of Recreational Mathematics as well as other mathematics-related journals.
In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers raised to the power k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers. Waring's problem was proposed in 1770 by Edward ...