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## Homework Statement

Prove that there is no positive ℚ = a s.t a*a*a= 2

## Homework Equations

## The Attempt at a Solution

If a = j/k a is in lowest form then one of j or k is odd.

(j^3/k^3) = 2 = j^3=2k^3 letting k^3 = z,

j^3 = 2z so j is even because an even number squared is even, thus an even number cubed is even.

Let j = 2i

so 8i^3=2k^3 = 2(2i^3) = k^3

so k is even for same reason as above.

Because k and j are both even, there is no positive ℚ = a s.t a*a*a= 2

Does my proof work?