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A Javascript solution:

const gcd = (n, d) => { return d === 0 ? n : gcd(d, n % d); } const proper_fractions = (d) => { if (d === 0 || d === 1) { return 0; } if (d === 2) { return 1; } let count = 0; let n = 0; while (n < d) { if (gcd(n, d) === 1) { count++; } n++; } return count; } console.log('Test cases'); console.log(`if d = 1, result: ${proper_fractions(1)}`); console.log(`if d = 2, result: ${proper_fractions(2)}`); console.log(`if d = 5, result: ${proper_fractions(5)}`); console.log(`if d = 15, result: ${proper_fractions(15)}`); console.log(`if d = 25, result: ${proper_fractions(25)}`);

Test cases:

if d = 1, result: 0 if d = 2, result: 1 if d = 5, result: 4 if d = 15, result: 8 if d = 25, result: 20

This is a pretty straight-forward solution using a counter. You can run this in vscode terminal as node [file-name].js

node [file-name].js

A Javascript solution:

Test cases:

This is a pretty straight-forward solution using a counter. You can run this in vscode terminal as

`node [file-name].js`