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The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
The predecessor of a natural number (excluding zero) is the previous natural number and is the result of subtracting one from that number. For example, the successor of zero is one, and the predecessor of eleven is ten ( 0 + 1 = 1 {\displaystyle 0+1=1} and 11 − 1 = 10 {\displaystyle 11-1=10} ).
As with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system.Each radix four, eight, and sixteen is a power of two, so the conversion to and from binary is implemented by matching each digit with two, three, or four binary digits, or bits.
In this case, s is called the least absolute remainder. [3] As with the quotient and remainder, k and s are uniquely determined, except in the case where d = 2n and s = ± n. For this exception, we have: a = k⋅d + n = (k + 1)d − n. A unique remainder can be obtained in this case by some convention—such as always taking the positive value ...
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
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