How many numbers from 1 to 200 inclusive are equal to the cube of an integer?


From 1 to 200 there are 5 perfect cubes.

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Cube Integers

Number theory (or arithmetic) is a branch of pure mathematics devoted primarily to the study of the integers, sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers).

Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (e.g., the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, e.g., as approximated by the latter (Diophantine approximation).

The Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties derived from its origin in Number Theory. Mathematically they are similar to the hypercube graphs, but with a Fibonacci number of vertices, studied in graph-theoretic mathematics. Fibonacci cubes were first explicitly defined in Hsu (1993) in the context of interconnection topologies for connecting parallel or distributed systems. They have also been applied in chemical graph theory.

The Fibonacci cube may be defined in terms of Fibonacci codes and Hamming distance, independent sets of vertices in path graphs, or via distributive lattices.

Intelligent Qube (アイキュー Aikyū?) is a puzzle game for the PlayStation. It is known as Kurushi in Europe and Australia. In the game, the player controls a character who must run around a platform made of cubes, clearing certain cubes as they approach. Cubes are "cleared" by marking a spot on the stage, waiting for the cube to roll on top of it, and then deactivating the marked spot.

Intelligent Qube was well received by critics. The game performed well commercially in Japan and even won Excellence Award for Interactive Art at the 1997 Japan Media Arts Festival. A few sequels have been developed and the game has since been re-released on mobile phones and the Japanese and European versions of the PlayStation Store.

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In recreational mathematics, a magic square is an arrangement of numbers (usually integers) in a square grid, where the numbers in each row, and in each column, and the numbers in the forward and backward main diagonals, all add up to the same number. A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows (and columns) it has. Thus, a magic square always contains n2 numbers, and its size (the number of rows [and columns] it has) is described as being "of order n". A magic square that contains the integers from 1 to n2 is called a normal magic square. (The term "magic square" is also sometimes used to refer to any of various types of word squares.)

It is possible to construct a normal magic square of any size except 2 × 2 (that is, where n = 2), although the solution to a magic square where n = 1 is trivial, since it consists simply of a single cell containing the number 1. The smallest nontrivial case, shown below, is a 3 × 3 grid (that is, a magic square of order 3).

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