MHB Can a Non-Integer Exponent be Used to Solve a Polynomial Equation?

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Not sure if this is the right place but could somebody help me solve the following equation
B.x^b - x - A =0 wher A, B and b are constants.
Thanks
 
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NY99 said:
Not sure if this is the right place but could somebody help me solve the following equation
B.x^b - x - A =0 wher A, B and b are constants.
Thanks

Welcome on MHB NY99!...

... if b is integer not exceeding 4, then it exist a procedure for algebraic solutions ... otherwise generally the solutions have to be found numerically ... the same is if b is not an integer...

Kind regards

$\chi$ $\sigma$
 
Thanks for that. Unfortunately b is not an integer so I guess It will have to be numerically solved.
 
Thread 'Determine whether ##125## is a unit in ##\mathbb{Z_471}##'

Thread 'Determine whether ##125## is a unit in ##\mathbb{Z_471}##'

This is the question, I understand the concept, in ##\mathbb{Z_n}## an element is a is a unit if and only if gcd( a,n) =1. My understanding of backwards substitution, ... i have using Euclidean algorithm, ##471 = 3⋅121 + 108## ##121 = 1⋅108 + 13## ##108 =8⋅13+4## ##13=3⋅4+1## ##4=4⋅1+0## using back-substitution, ##1=13-3⋅4## ##=(121-1⋅108)-3(108-8⋅13)## ... ##= 121-(471-3⋅121)-3⋅471+9⋅121+24⋅121-24(471-3⋅121## ##=121-471+3⋅121-3⋅471+9⋅121+24⋅121-24⋅471+72⋅121##...
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