The number `n` for which number of dissimilar terms in the expansion of `(1+x+x^(2)+x^(3))^(n)` is equal to number of terms in the expansion of `(x+y+z)^(n)` is `(nepsilonN)`

Answer

3

Explanation

Number of terms in the exp. Of `(1+x+x^(2)+x^(3))^(n)=3n+1`
Number of terms in the exp. Of `(x+y+z)^(n)=^(n+2)C_(2)`
`implies^(n+2)C_(2)=3n+1`
`(n+2)(n+1)=6n+2:n^(2)+3n+2=6n+2`
`n^(2)=3nimpliesn=0` or `3, because n in N impliesn=3`