RMO 2015!

Algebra Level 4

{(1+x)(1+x2)(1+x4)=1+y7(1+y)(1+y2)(1+y4)=1+x7 \begin{cases} \begin{aligned} (1 + x)\big(1 + x^2\big)\big(1 + x^4\big) &= 1 + y^7 \\\\ (1 + y)\big(1 + y^2\big)\big(1 + y^4\big) &= 1 + x^7 \end{aligned} \end{cases}

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

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