{"status": "success", "data": {"description_md": "**POTD October 27, 2024**\n\nFind the smallest positive number $\\lambda$ , such that for any complex numbers ${z_1},{z_2},{z_3}\\in\\{z\\in \\mathbb{C}\\;\\big|\\;|z|<1\\}$, if $z_1+z_2+z_3=0$, then$$\\left|z_1z_2 +z_2z_3+z_3z_1\\right|^2+\\left|z_1z_2z_3\\right|^2 <\\lambda .$$", "description_html": "<p><strong>POTD October 27, 2024</strong></p>&#10;<p>Find the smallest positive number <span class=\"katex--inline\">\\lambda</span> , such that for any complex numbers <span class=\"katex--inline\">{z_1},{z_2},{z_3}\\in\\{z\\in \\mathbb{C}\\;\\big|\\;|z|&lt;1\\}</span>, if <span class=\"katex--inline\">z_1+z_2+z_3=0</span>, then<span class=\"katex--display\">\\left|z_1z_2 +z_2z_3+z_3z_1\\right|^2+\\left|z_1z_2z_3\\right|^2 &lt;\\lambda .</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 9, "problem_name": "Problem of the Day #314", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}