fix(curriculum): clean-up Project Euler 441-460 (#43068)
* fix: clean-up Project Euler 441-460 * 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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@ -8,20 +8,26 @@ dashedName: problem-446-retractions-b
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# --description--
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For every integer n>1, the family of functions fn,a,b is defined
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For every integer $n > 1$, the family of functions $f_{n, a, b}$ is defined by:
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by fn,a,b(x)≡ax+b mod n for a,b,x integer and 0
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$f_{n, a, b}(x) ≡ ax + b\bmod n$ for $a, b, x$ integer and $0 \lt a \lt n$, $0 \le b \lt n$, $0 \le x \lt n$.
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F(N)=∑R(n4+4) for 1≤n≤N. F(1024)=77532377300600.
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We will call $f_{n, a, b}$ a retraction if $f_{n, a, b}(f_{n, a, b}(x)) \equiv f_{n, a, b}(x)\bmod n$ for every $0 \le x \lt n$.
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Find F(107) (mod 1 000 000 007)
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Let $R(n)$ be the number of retractions for $n$.
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$F(N) = \displaystyle\sum_{n = 1}^N R(n^4 + 4)$.
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$F(1024) = 77\\,532\\,377\\,300\\,600$.
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Find $F({10}^7)$. Give your answer modulo $1\\,000\\,000\\,007$.
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# --hints--
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`euler446()` should return 907803852.
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`retractionsB()` should return `907803852`.
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```js
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assert.strictEqual(euler446(), 907803852);
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assert.strictEqual(retractionsB(), 907803852);
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```
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# --seed--
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@ -29,12 +35,12 @@ assert.strictEqual(euler446(), 907803852);
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## --seed-contents--
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```js
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function euler446() {
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function retractionsB() {
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return true;
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}
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euler446();
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retractionsB();
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```
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# --solutions--
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