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In mathematics, a square number or perfect square is an integer that is the square of an integer; [1] in other words, ... 54 2 = 2916 55 2 = 3025 56 2 = 3136 57 2 = 3249
[54] Every even perfect number ends in 6 or 28, base ten; and, with the only exception of 6, ends in 1 in base 9. [55] [56] Therefore, in particular the digital root of every even perfect number other than 6 is 1. The only square-free perfect number is 6. [57]
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]
54 is the smallest number that can be written as the sum of three positive squares in more than two different ways: 72 + 22 + 12 = 62 + 32 + 32 = 52 + 52 + 22 = 54. [3][4] It is a 19- gonal number, [5] In base 10, 54 is a Harshad number. [6] The Holt graph has 54 edges. The sine of an angle of 54 degrees is half the golden ratio.
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...
The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.
A perfect square is an element of algebraic structure that is equal to the square of another element. Square number, a perfect square integer. Entertainment
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. This shows that the square of the n th triangular number is equal to the sum of the first n cube numbers. Also, the square of the n th triangular number is the same as the sum of the cubes of the integers 1 to n.