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In 1747, Leonhard Euler completed what is now called the Euclid–Euler theorem, showing that these are the only even perfect numbers. As a result, there is a one-to-one correspondence between Mersenne primes and even perfect numbers, so a list of one can be converted into a list of the other. [1] [5] [6]
A most-perfect magic square of order n is a magic square containing the numbers 1 to n 2 with two additional properties: Each 2 × 2 subsquare sums to 2 s , where s = n 2 + 1. All pairs of integers distant n /2 along a (major) diagonal sum to s .
A peculiarity of the construction method given above for the odd magic squares is that the middle number (n 2 + 1)/2 will always appear at the center cell of the magic square. Since there are (n − 1)! ways to arrange the skew diagonal terms, we can obtain (n − 1)! Greek squares this way; same with the Latin squares.
Square number 16 as sum of gnomons. In mathematics, a square number or perfect square is an integer that is the square of an integer; [1] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3 2 and can be written as 3 × 3.
Klauber's 1932 paper describes a triangle in which row n contains the numbers (n − 1) 2 + 1 through n 2. As in the Ulam spiral, quadratic polynomials generate numbers that lie in straight lines. Vertical lines correspond to numbers of the form k 2 − k + M. Vertical and diagonal lines with a high density of prime numbers are evident in the ...
Notably, absent consensus, please do not add articles about individual perfect numbers themselves (such as 6). Pages in category "Perfect numbers" The following 11 pages are in this category, out of 11 total.
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A powerful number is a positive integer m such that for every prime number p dividing m, p 2 also divides m.Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a 2 b 3, where a and b are positive integers.