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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:
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. The equation is named after Srinivasa Ramanujan , who conjectured that it has only five integer solutions, and after Trygve Nagell , who proved the conjecture.
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 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 ...
For example, the equation = has the solution = Raising both sides to the exponent of 2 (which means applying the function f ( s ) = s 2 {\displaystyle f(s)=s^{2}} to both sides of the equation) changes the equation to x 2 = 1 {\displaystyle x^{2}=1} , which not only has the previous solution but also introduces the extraneous solution, x = − ...
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The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law.The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra.
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.
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