{"status": "success", "data": {"description_md": "The function $f$, defined on the set of ordered pairs of positive integers, satisfies the following properties:\n - $f(x,x) = x$\n - $f(x,y) = f(y,x)$\n - $(x + y) f(x,y) = yf(x,x + y)$. \n\nCalculate $f(14,52)$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The function <span class=\"katex--inline\">f</span>, defined on the set of ordered pairs of positive integers, satisfies the following properties:</p>&#10;<ul>&#10;<li><span class=\"katex--inline\">f(x,x) = x</span></li>&#10;<li><span class=\"katex--inline\">f(x,y) = f(y,x)</span></li>&#10;<li><span class=\"katex--inline\">(x + y) f(x,y) = yf(x,x + y)</span>.</li>&#10;</ul>&#10;<p>Calculate <span class=\"katex--inline\">f(14,52)</span>.</p>&#10;<hr/>&#10;<p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "1988 AIME Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/88_aime_p09", "prev": "/problem/88_aime_p07"}}