49 lines
1.2 KiB
Markdown
49 lines
1.2 KiB
Markdown
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---
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id: 5900f4c81000cf542c50ffd9
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title: 'Problem 347: Largest integer divisible by two primes'
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challengeType: 5
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forumTopicId: 302006
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dashedName: problem-347-largest-integer-divisible-by-two-primes
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---
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# --description--
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The largest integer $≤ 100$ that is only divisible by both the primes 2 and 3 is 96, as $96 = 32 \times 3 = 2^5 \times 3$.
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For two distinct primes $p$ and $q$ let $M(p, q, N)$ be the largest positive integer $≤ N$ only divisible by both $p$ and $q$ and $M(p, q, N)=0$ if such a positive integer does not exist.
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E.g. $M(2, 3, 100) = 96$.
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$M(3, 5, 100) = 75$ and not 90 because 90 is divisible by 2, 3 and 5. Also $M(2, 73, 100) = 0$ because there does not exist a positive integer $≤ 100$ that is divisible by both 2 and 73.
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Let $S(N)$ be the sum of all distinct $M(p, q, N)$. $S(100)=2262$.
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Find $S(10\\,000\\,000)$.
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# --hints--
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`integerDivisibleByTwoPrimes()` should return `11109800204052`.
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```js
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assert.strictEqual(integerDivisibleByTwoPrimes(), 11109800204052);
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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 integerDivisibleByTwoPrimes() {
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return true;
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}
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integerDivisibleByTwoPrimes();
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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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