RMO 2015!

Algebra Level 5

\[\large{ \begin{cases}(1 + x)(1 + x^2)(1 + x^4) = 1 + y^7 \\ (1 + y)(1 + y^2)(1 + y^4) = 1 + x^7 \end{cases}}\]

Find the number of ordered pairs of real numbers \((x, y)\) for which the above system of equations satisfy.

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