self Maths Puzzle

Find the remainder when 34^413 is divided by 9

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self Other Question

suppose we are given three relations.
a+b+c=X
ab+bc+ca=Y
abc=Z
X,Y,Z are known, how can we find a,b,c
we are given the values of three relations.
a+b+c=X
ab+bc+ca=Y
abc=Z
knowing X,Y & Z how can we find a,b,c?