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The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .
In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. [2] [3] The integers k of this form are sometimes referred to as totatives of n. For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8.
Substituting r(cos θ + i sin θ) for e ix and equating real and imaginary parts in this formula gives dr / dx = 0 and dθ / dx = 1. Thus, r is a constant, and θ is x + C for some constant C. The initial values r(0) = 1 and θ(0) = 0 come from e 0i = 1, giving r = 1 and θ = x.
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The Schur multiplier of E 7 (q) is gcd(2, q−1), and its outer automorphism group is the product of the diagonal automorphism group Z/gcd(2, q−1)Z (given by the action of E 7,ad (q)) and the group of field automorphisms (i.e., cyclic of order f if q = p f where p is prime).
(The Center Square) – The New York judge overseeing President-elect Donald Trump's hush money case said Monday he won't toss Trump's conviction. Judge Juan Merchan denied Trump's motion to ...
Sen. Chuck Grassley, the Republican slated to lead the Judiciary Committee next year, blasted FBI Director Christopher Wray in terms echoing Trump.