60 lines
1.1 KiB
Markdown
60 lines
1.1 KiB
Markdown
---
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id: 5900f5111000cf542c510023
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title: 'Problem 420: 2x2 positive integer matrix'
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challengeType: 5
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forumTopicId: 302090
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dashedName: problem-420-2x2-positive-integer-matrix
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---
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# --description--
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A positive integer matrix is a matrix whose elements are all positive integers.
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Some positive integer matrices can be expressed as a square of a positive integer matrix in two different ways. Here is an example:
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$$\begin{pmatrix}
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40 & 12 \\\\
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48 & 40
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\end{pmatrix} =
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{\begin{pmatrix}
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2 & 3 \\\\
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12 & 2
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\end{pmatrix}}^2 =
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{\begin{pmatrix}
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6 & 1 \\\\
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4 & 6
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\end{pmatrix}}^2$$
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We define $F(N)$ as the number of the 2x2 positive integer matrices which have a trace less than N and which can be expressed as a square of a positive integer matrix in two different ways.
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We can verify that $F(50) = 7$ and $F(1000) = 1019$.
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Find $F({10}^7)$.
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# --hints--
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`positiveIntegerMatrix()` should return `145159332`.
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```js
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assert.strictEqual(positiveIntegerMatrix(), 145159332);
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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 positiveIntegerMatrix() {
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return true;
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}
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positiveIntegerMatrix();
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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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