{"status": "success", "data": {"description_md": "Find the sum of all primes $p$ such that there exists a positive integer $a$ such that\n$$\\left \\lfloor \\dfrac{a}{p} \\right \\rfloor+\\left \\lfloor \\dfrac{2a}{p} \\right \\rfloor+\\cdots+\\left \\lfloor \\dfrac{pa}{p} \\right \\rfloor = 100. $$", "description_html": "<p>Find the sum of all primes <span class=\"katex--inline\">p</span> such that there exists a positive integer <span class=\"katex--inline\">a</span> such that<br/>&#10;<span class=\"katex--display\">\\left \\lfloor \\dfrac{a}{p} \\right \\rfloor+\\left \\lfloor \\dfrac{2a}{p} \\right \\rfloor+\\cdots+\\left \\lfloor \\dfrac{pa}{p} \\right \\rfloor = 100.</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Christmas Contest - Individual Round - Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_individual-p18", "prev": "/problem/christmas1_individual-p16"}}