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fix(curriculum): clean-up Project Euler 201-220 (#42826)

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* fix: clean-up Project Euler 201-220

* fix: corrections from review

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
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gikf
2021-07-15 09:20:31 +02:00
committed by GitHub
parent 505c3b7c6c
commit eef1805fe6
20 changed files with 254 additions and 156 deletions
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27
curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-214-totient-chains.md
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@ -8,24 +8,31 @@ dashedName: problem-214-totient-chains
# --description--
Let φ be Euler's totient function, i.e. for a natural number n,
Let $φ$ be Euler's totient function, i.e. for a natural number $n$, $φ(n)$ is the number of $k$, $1 ≤ k ≤ n$, for which $gcd(k,n) = 1$.
φ(n) is the number of k, 1 ≤ k ≤ n, for which gcd(k,n) = 1.
By iterating $φ$, each positive integer generates a decreasing chain of numbers ending in 1. E.g. if we start with 5 the sequence 5,4,2,1 is generated. Here is a listing of all chains with length 4:
By iterating φ, each positive integer generates a decreasing chain of numbers ending in 1. E.g. if we start with 5 the sequence 5,4,2,1 is generated. Here is a listing of all chains with length 4:
5,4,2,1 7,6,2,1 8,4,2,1 9,6,2,1 10,4,2,1 12,4,2,1 14,6,2,1 18,6,2,1
$$\begin{align}
5,4,2,1 & \\\\
7,6,2,1 & \\\\
8,4,2,1 & \\\\
9,6,2,1 & \\\\
10,4,2,1 & \\\\
12,4,2,1 & \\\\
14,6,2,1 & \\\\
18,6,2,1 &
\end{align}$$
Only two of these chains start with a prime, their sum is 12.
What is the sum of all primes less than 40000000 which generate a chain of length 25?
What is the sum of all primes less than $40\\,000\\,000$ which generate a chain of length 25?
# --hints--
`euler214()` should return 1677366278943.
`totientChains()` should return `1677366278943`.
```js
assert.strictEqual(euler214(), 1677366278943);
assert.strictEqual(totientChains(), 1677366278943);
```
# --seed--
@ -33,12 +40,12 @@ assert.strictEqual(euler214(), 1677366278943);
## --seed-contents--
```js
function euler214() {
function totientChains() {
return true;
}
euler214();
totientChains();
```
# --solutions--