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The number of elements in a reduced residue system is (), where is the Euler totient function, i.e., the number of positive integers less than m that are relatively prime to m. In a general ring with unity not every element has a multiplicative inverse and those that do are called units.
Python supports normal floating point numbers, which are created when a dot is used in a literal (e.g. 1.1), when an integer and a floating point number are used in an expression, or as a result of some mathematical operations ("true division" via the / operator, or exponentiation with a negative exponent).
Primitive root modulo m: A number g is a primitive root modulo m if, for every integer a coprime to m, there is an integer k such that g k ≡ a (mod m). A primitive root modulo m exists if and only if m is equal to 2, 4, p k or 2p k, where p is an odd prime number and k is a positive integer.
Lighting and reflection calculations, as in the video game OpenArena, use the fast inverse square root code to compute angles of incidence and reflection.. Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in ...
A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. This process is sometimes called the 196-algorithm , after the most famous number associated with the process.
In the random-access machine commonly used in algorithm analysis, a simple algorithm that scans the indexes in input order and swaps whenever the scan encounters an index whose reversal is a larger number would perform a linear number of data moves. [10] However, computing the reversal of each index may take a non-constant number of steps.
A number that is non-palindromic in all bases b in the range 2 ≤ b ≤ n − 2 can be called a strictly non-palindromic number. For example, the number 6 is written as "110" in base 2, "20" in base 3, and "12" in base 4, none of which are palindromes. All strictly non-palindromic numbers larger than 6 are prime.
An emirp (an anadrome of prime) is a prime number that results in a different prime when its decimal digits are reversed. [1] This definition excludes the related palindromic primes . The term reversible prime is used to mean the same as emirp, but may also, ambiguously, include the palindromic primes.