{"status": "success", "data": {"description_md": "Find the number of solutions for $x, y, z \\in \\mathbb{Z}^+$ to $$x^{1434}+y^{1434}=z^{1434} $$", "description_html": "<p>Find the number of solutions for <span class=\"katex--inline\">x, y, z \\in \\mathbb{Z}^+</span> to <span class=\"katex--display\">x^{1434}+y^{1434}=z^{1434}</span></p>&#10;", "hints_md": "Andrew Wiles.", "hints_html": "<p>Andrew Wiles.</p>&#10;", "editorial_md": "Fermat\u2019s Last Theorem, proven by Andrew Wiles, states that there are no three positive integers $a$, $b$ and $c$ that can satisfy the equation $a^n+b^n=c^n$ for any integer value of $n$ greater than 2.\n\nGiven that our exponent $1434$ is significantly greater than $2$, Fermat\u2019s Last Theorem tells us that there are no positive integer solutions for $x$, $y$ and $z$ that can satisfy this equation.\n\nTherfore our answer is $0$.\n\n- botman", "editorial_html": "<p>Fermat&#8217;s Last Theorem, proven by Andrew Wiles, states that there are no three positive integers <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span> and <span class=\"katex--inline\">c</span> that can satisfy the equation <span class=\"katex--inline\">a^n+b^n=c^n</span> for any integer value of <span class=\"katex--inline\">n</span> greater than 2.</p>&#10;<p>Given that our exponent <span class=\"katex--inline\">1434</span> is significantly greater than <span class=\"katex--inline\">2</span>, Fermat&#8217;s Last Theorem tells us that there are no positive integer solutions for <span class=\"katex--inline\">x</span>, <span class=\"katex--inline\">y</span> and <span class=\"katex--inline\">z</span> that can satisfy this equation.</p>&#10;<p>Therfore our answer is <span class=\"katex--inline\">0</span>.</p>&#10;<ul>&#10;<li>botman</li>&#10;</ul>&#10;", "flag_hint": "", "point_value": 1, "problem_name": "You're Lucky this isn't Proof Based", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}