Let $a \geq b, a \geq c$ Then $\frac{b+c}{c} \geq \frac{a+b}{b} \to \frac{b}{c} \geq \frac{a}{b} \geq 1 \to b \geq c$ $\frac{a+c}{a} \geq \frac{a+b}{b} \to \frac{c}{a} \geq \frac {a}{b} \to bc \geq a^2 \to a=b=c$ And so $a=b=c=2^{2019}$