49 lines
972 B
Markdown
49 lines
972 B
Markdown
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---
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id: 5900f4791000cf542c50ff8c
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title: 'Problem 269: Polynomials with at least one integer root'
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challengeType: 5
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forumTopicId: 301918
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dashedName: problem-269-polynomials-with-at-least-one-integer-root
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---
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# --description--
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A root or zero of a polynomial P(x) is a solution to the equation P(x) = 0.
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Define Pn as the polynomial whose coefficients are the digits of n.
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For example, P5703(x) = 5x3 + 7x2 + 3.
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We can see that:Pn(0) is the last digit of n, Pn(1) is the sum of the digits of n, Pn(10) is n itself.Define Z(k) as the number of positive integers, n, not exceeding k for which the polynomial Pn has at least one integer root.
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It can be verified that Z(100 000) is 14696.
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What is Z(1016)?
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# --hints--
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`euler269()` should return 1311109198529286.
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```js
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assert.strictEqual(euler269(), 1311109198529286);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler269() {
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return true;
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}
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euler269();
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```
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# --solutions--
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```js
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// solution required
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```
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