{"status": "success", "data": {"description_md": "**POTD October 23, 2024**\n\nIf the greatest real number $R$ such that for every positive integer $n \\ge 2$, there exists reals $x_1, x_2, \\ldots, x_n \\in [-1, 1]$ so that $$\\prod\\limits_{1 \\le i < j \\le n} (x_i-x_j) \\ge R^{\\frac{n(n-1)}{2}}$$ can be expressed as $\\dfrac{a}{b}$, where $a$ and $b$ are relatively prime, positive integers, compute $a+b$.", "description_html": "<p><strong>POTD October 23, 2024</strong></p>&#10;<p>If the greatest real number <span class=\"katex--inline\">R</span> such that for every positive integer <span class=\"katex--inline\">n \\ge 2</span>, there exists reals <span class=\"katex--inline\">x_1, x_2, \\ldots, x_n \\in [-1, 1]</span> so that <span class=\"katex--display\">\\prod\\limits_{1 \\le i &lt; j \\le n} (x_i-x_j) \\ge R^{\\frac{n(n-1)}{2}}</span> can be expressed as <span class=\"katex--inline\">\\dfrac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime, positive integers, compute <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 8, "problem_name": "Problem of the Day #310", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}