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64 is: the smallest number with exactly seven divisors, [3] the first whole number (greater than one) that is both a perfect square, and a perfect cube, [4] the lowest positive power of two that is not adjacent to either a Mersenne prime or a Fermat prime, the fourth superperfect number — a number such that σ(σ(n)) = 2n, [5]
A crossword (or crossword puzzle) is a word game consisting of a grid of black and white squares, into which solvers enter words or phrases ("entries") crossing each other horizontally ("across") and vertically ("down") according to a set of clues. Each white square is typically filled with one letter, while the black squares are used to ...
These numbers, borrowing crossword terminology, are commonly called "clues". The objective of the puzzle is to insert a digit from 1 to 9 inclusive into each white cell so that the sum of the numbers in each entry matches the clue associated with it and that no digit is duplicated in any entry.
A non-negative integer is a square number when its square root is again an integer. For example, =, so 9 is a square number. A positive integer that has no square divisors except 1 is called square-free. For a non-negative integer n, the n th square number is n 2, with 0 2 = 0 being the zeroth one. The concept of square can be extended to some ...
If n is an even superperfect number, then n must be a power of 2, 2 k, such that 2 k+1 − 1 is a Mersenne prime. [1] [2] It is not known whether there are any odd superperfect numbers. An odd superperfect number n would have to be a square number such that either n or σ(n) is divisible by at least three distinct primes. [2]
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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 ...