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In mathematics, a character sum is a sum () of values of a Dirichlet character χ modulo N, taken over a given range of values of n.Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo N.
Thus, the Ramanujan sum c q (n) is the sum of the n-th powers of the primitive q-th roots of unity. It is a fact [3] that the powers of ζ q are precisely the primitive roots for all the divisors of q. Example. Let q = 12. Then
Rufus was originally designed [5] as a modern open source replacement for the HP USB Disk Storage Format Tool for Windows, [6] which was primarily used to create DOS bootable USB flash drives. The first official release of Rufus, version 1.0.3 (earlier versions were internal/alpha only [ 7 ] ), was released on December 04, 2011, with originally ...
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The phrase "IBM PC compatible self-booting disk" is sometimes shortened to "PC booter". Self-booting disks were common for other computers as well. These games were distributed on 5 + 1 ⁄ 4 " or, later, 3 + 1 ⁄ 2 ", floppy disks that booted directly, meaning once they were inserted in the drive and the computer was turned on, a minimal ...
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Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series.Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties that make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.
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