{"status": "success", "data": {"description_md": "For all ordered pairs of positive integers $(x,y)$ such that $$\\frac{x^{3}+2x^{2}y^{2}-xy^{2}-2y^{4}}{x+2y^{2}} = 2025,$$\n\nwhere $x>y,$ what is the sum of all possible positive integers $x$?", "description_html": "<p>For all ordered pairs of positive integers <span class=\"katex--inline\">(x,y)</span> such that <span class=\"katex--display\">\\frac{x^{3}+2x^{2}y^{2}-xy^{2}-2y^{4}}{x+2y^{2}} = 2025,</span></p>&#10;<p>where <span class=\"katex--inline\">x&gt;y,</span> what is the sum of all possible positive integers <span class=\"katex--inline\">x</span>?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Mock Euclid 2025 - Problem 7 Part A", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}