Do A/<b(x)> and A/<c(x)> have the same number of elements?

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Let A be the integers modulo 7.
b(x)= x^3 -2 and c(x) = x^3 + 2 are polynomials in A[x].

How can you show that A/<b(x)> and A/<c(x)> have the same number of elements? In this practice problem I already showed that A/<b(x)> and A/<c(x)> are fields by showing that <b(x)> and <c(x)> are maximal ideals, but I don't know how this helps.
 
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you stated it wrong it seems. you want A[x]/<whatever>. then it gets easier.
 
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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