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A solution (a, b, c) for a given n leads to a solution for all the factors of n: if h is a factor of n then there is an integer g such that n = gh. Then (a g, b g, c g) is a solution for the exponent h: (a g) h + (b g) h = (c g) h.
In the base ten number system, integer powers of 10 are written as the digit 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, 10 3 = 1000 and 10 −4 = 0.0001. Exponentiation with base 10 is used in scientific notation to denote large or small numbers.
A quadratic equation is one which includes a term with an exponent of 2, for example, , [40] and no term with higher exponent. The name derives from the Latin quadrus , meaning square. [ 41 ] In general, a quadratic equation can be expressed in the form a x 2 + b x + c = 0 {\displaystyle ax^{2}+bx+c=0} , [ 42 ] where a is not zero (if it were ...
In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
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 forma+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.
In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two.It is an example of an exponential Diophantine equation, an equation to be solved in integers where one of the variables appears as an exponent.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
In arithmetic and algebra, the seventh power of a number n is the result of multiplying seven instances of n together. So: n 7 = n × n × n × n × n × n × n.. Seventh powers are also formed by multiplying a number by its sixth power, the square of a number by its fifth power, or the cube of a number by its fourth power.
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