{"status": "success", "data": {"description_md": "A *lattice point* is a point with integer coordinates. (For example, $(1,4)$ is a lattice point but $(\\frac{3}{2},4)$ is not.) The line $y = 3x - 5$ passes through square $PQRS$ as shown in the diagram. If the coordinates of $R$ are $(2009, 2009)$, then the number of lattice points on the line which are inside the square is\n\n<center><img class=\"problem-image\" src=\"/static/cayley/2009/crops/09_cayley_p21_fig.png\" alt=\"figure\" width=\"294\"></center>\n\n$\\text{(A)}\\ 666\\qquad\\text{(B)}\\ 667\\qquad\\text{(C)}\\ 668\\qquad\\text{(D)}\\ 669\\qquad\\text{(E)}\\ 670$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>A *lattice point* is a point with integer coordinates. (For example, <span class=\"katex--inline\">(1,4)</span> is a lattice point but <span class=\"katex--inline\">(\\frac{3}{2},4)</span> is not.) The line <span class=\"katex--inline\">y = 3x - 5</span> passes through square <span class=\"katex--inline\">PQRS</span> as shown in the diagram. If the coordinates of <span class=\"katex--inline\">R</span> are <span class=\"katex--inline\">(2009, 2009)</span>, then the number of lattice points on the line which are inside the square is</p>\n<center><img class=\"problem-image\" src=\"/static/cayley/2009/crops/09_cayley_p21_fig.png\" alt=\"figure\" width=\"294\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 666\\qquad\\text{(B)}\\ 667\\qquad\\text{(C)}\\ 668\\qquad\\text{(D)}\\ 669\\qquad\\text{(E)}\\ 670</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2009 Cayley Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/09_cayley_p22", "prev": "/problem/09_cayley_p20"}}