{"status": "success", "data": {"description_md": "Three distinct integers $a$, $b$ and $c$ satisfy the following three conditions:\n\n- $abc = 17\\,955$,\n- $a$, $b$ and $c$ form an arithmetic sequence in that order, and\n- $(3a + b)$, $(3b + c)$, and $(3c + a)$ form a geometric sequence in that order.\n\nWhat is the value of $a + b + c$?\n\n(An *arithmetic sequence* is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, $3, 5, 7$ is an arithmetic sequence with three terms.\nA *geometric sequence* is a sequence in which each term after the first is obtained from the previous term by multiplying it by a non-zero constant. For example, $3, 6, 12$ is a geometric sequence with three terms.)\n\n$\\text{(A)}\\ -63\\qquad\\text{(B)}\\ -42\\qquad\\text{(C)}\\ -68\\,229\\qquad\\text{(D)}\\ -48\\qquad\\text{(E)}\\ 81$\n\n___\n\n**[Fermat](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>Three distinct integers <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span> and <span class=\"katex--inline\">c</span> satisfy the following three conditions:</p>\n<p>- <span class=\"katex--inline\">abc = 17\\,955</span>,\n- <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span> and <span class=\"katex--inline\">c</span> form an arithmetic sequence in that order, and\n- <span class=\"katex--inline\">(3a + b)</span>, <span class=\"katex--inline\">(3b + c)</span>, and <span class=\"katex--inline\">(3c + a)</span> form a geometric sequence in that order.</p>\n<p>What is the value of <span class=\"katex--inline\">a + b + c</span>?</p>\n<p>(An *arithmetic sequence* is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, <span class=\"katex--inline\">3, 5, 7</span> is an arithmetic sequence with three terms.\nA *geometric sequence* is a sequence in which each term after the first is obtained from the previous term by multiplying it by a non-zero constant. For example, <span class=\"katex--inline\">3, 6, 12</span> is a geometric sequence with three terms.)</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ -63\\qquad\\text{(B)}\\ -42\\qquad\\text{(C)}\\ -68\\,229\\qquad\\text{(D)}\\ -48\\qquad\\text{(E)}\\ 81</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Fermat</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": "2015 Fermat Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/15_fermat_p23", "prev": "/problem/15_fermat_p21"}}