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All centered square numbers and their divisors have a remainder of 1 when divided by 4. Hence all centered square numbers and their divisors end with digit 1 or 5 in base 6, 8, and 12. Every centered square number except 1 is the hypotenuse of a Pythagorean triple (3-4-5, 5-12-13, 7-24-25, ...). This is exactly the sequence of Pythagorean ...
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 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. Powerful numbers are also known as squareful, square-full, or 2-full.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
So too are the thousands, with the number of thousands followed by the word "thousand". The number one thousand may be written 1 000 or 1000 or 1,000; larger numbers are written for example 10 000 or 10,000 for ease of reading. European languages that use the comma as a decimal separator may correspondingly use the period as a thousands separator.
1000 or one thousand is the natural number following 999 and preceding 1001.In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
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A number where some but not all prime factors have multiplicity above 1 is neither square-free nor squareful. The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd. The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd.