{"status": "success", "data": {"description_md": "**POTD March 26, 2024**\n\nGiven that $w$ and $z$ are complex numbers such that $|w + z| = 1$ and $|w^2 + z^2| = 14,$ then the smallest possible value of $|w^3 + z^3|$ can be written as $\\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Find $a+b$.", "description_html": "<p><strong>POTD March 26, 2024</strong></p>&#10;<p>Given that <span class=\"katex--inline\">w</span> and <span class=\"katex--inline\">z</span> are complex numbers such that <span class=\"katex--inline\">|w + z| = 1</span> and <span class=\"katex--inline\">|w^2 + z^2| = 14,</span> then the smallest possible value of <span class=\"katex--inline\">|w^3 + z^3|</span> can be written as <span class=\"katex--inline\">\\frac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime positive integers. Find <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #108", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}