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Let $x,y, z$ be relatively prime integers with $xyz \neq 0$. Suppose that

$$x^{m/n} + y^{m/n} = z^{m/n}$$

where $m,n$ are relatively prime integers with $mn \neq 0$.

Does it necessarily follow that $x,y,z$ are perfect $n$^th powers ?

Let $x,y, z$ be relatively prime integers with $xyz \neq 0$. Suppose that

$$x^{m/n} + y^{m/n} = z^{m/n}$$

where $m,n$ are relatively prime integers with $mn \neq 0$.

Does it necessarily follow that $x,y,z$ are perfect $n$-th powers ?

Let $x,y, z$ be relatively prime integers with $zyz\neq 0$. Suppose that

$$x^{m/n} + y^{m/n} = z^{m/n}$$

where $m,n$ are relatively prime integers with $mn\neq 0$.

Does it necessarily follow that $x,y,z$ are perfect $n$-th powers ?

Let $x,y, z$ be relatively prime integers with $xyz \neq 0$. Suppose that

$$x^{m/n} + y^{m/n} = z^{m/n}$$

where $m,n$ are relatively prime integers with $mn \neq 0$.

Does it necessarily follow that $x,y,z$ are perfect $n$^th powers ?

Let $x,y, z$ be relatively prime integers with $zyz\neq 0$. Suppose that

$$x^{m/n} + y^{m/n} = z^{m/n}$$

where $m,n$ are relatively prime integers with $mn\neq 0$.

Does it necessarily follow that $x,y,z$ are perfect $n-th$ powers ?

Let $x,y, z$ be relatively prime integers with $zyz\neq 0$. Suppose that

$$x^{m/n} + y^{m/n} = z^{m/n}$$

where $m,n$ are relatively prime integers with $mn\neq 0$.

Does it necessarily follow that $x,y,z$ are perfect $n$-th powers ?