# inequality – Prove that \$frac{1+x_1^2}{1+x_1x_2} + frac{1+x_2^2}{1+x_2x_3} + … + frac{1+x_{2020}^2}{1+x_{2020}x_{1}} geq 2020\$

Given $$x_1, x_2, …, x_{2020}$$ as positive real numbers. Prove that $$frac{1+x_1^2}{1+x_1x_2} + frac{1+x_2^2}{1+x_2x_3} + … + frac{1+x_{2020}^2}{1+x_{2020}x_{1}} geq 2020$$
Only use AM-GM, Cauchy-Schwarz and Bunyakovsky inequalities. No more than that.

Currently I don’t know anything besides the equal sign will occur when $$x_1=x_2=…=x_{2020}$$.