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[2] A superscript is understood to be grouped as long as it continues in the form of a superscript. For example if an x has a superscript of the form a+b, the sum is the exponent. For example: x 2+3, it is understood that the 2+3 is grouped, and that the exponent is the sum of 2 and 3. These rules are understood by all mathematicians.
[6] [7] [a] The parentheses can be omitted if the input is a single numerical variable or constant, [2] as in the case of sin x = sin(x) and sin π = sin(π). [a] Traditionally this convention extends to monomials; thus, sin 3x = sin(3x) and even sin 1 / 2 xy = sin(xy/2), but sin x + y = sin(x) + y, because x + y is not a monomial ...
For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 + 2x + 1. One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −x.
If two primes which end in 3 or 7 and surpass by 3 a multiple of 4 are multiplied, then their product will be composed of a square and the quintuple of another square. In other words, if p, q are of the form 20k + 3 or 20k + 7, then pq = x 2 + 5y 2. Euler later extended this to the conjecture that
The plus–minus sign, ±, is used as a shorthand notation for two expressions written as one, representing one expression with a plus sign, the other with a minus sign. For example, y = x ± 1 represents the two equations y = x + 1 and y = x − 1. Sometimes, it is used for denoting a positive-or-negative term such as ±x.
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x 1 = x; x 2 = x 2 for i = k - 2 to 0 do if n i = 0 then x 2 = x 1 * x 2; x 1 = x 1 2 else x 1 = x 1 * x 2; x 2 = x 2 2 return x 1 The algorithm performs a fixed sequence of operations ( up to log n ): a multiplication and squaring takes place for each bit in the exponent, regardless of the bit's specific value.
Cotter told the jury that the government’s math, its theory of what happened here, didn’t add up when the trial began about 15 weeks ago. After 65 witnesses and hundreds of exhibits, Cotter sai