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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 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 ...
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 ...
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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An impossible puzzle is a puzzle that cannot be resolved, either due to lack of sufficient information, or any number of logical impossibilities. 15 Puzzle – Slide fifteen numbered tiles into numerical order. It is impossible to solve in half of the starting positions. [1]
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But here, the context is the set of integers. If you consider that you should not have an implicit context, then the term perfect square is also ambiguous, because it is also used for non-integers, like here, where 102.01 is regarded as a perfect square because (10.1)² = 102.01 exactly. See also the footnote saying: "Some authors also call ...