IIT JEE , AIEEE Forum - Mathematics , Algebra - Give wuth justificationa natural no. n for which 3^9+3^12+3^15+3^n is a perfect cube

sriram.a

yaar very simple take 3^9(1+3^3+3^6+3^{n-9))=x^3
3^9(1+27+729+3^{n-9})=x^3
3^9is a cube 1+27+729+3^{n-9}) should be a perfect cube
757+3^{n-9})=x^3(x=10,11,12,13,14,................)
for x=10 n=14 the entire equatin becomes a perfect cube
for any other x there is no n such thatl equation is a perfect cube

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