972 B
972 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4091000cf542c50ff1c | Problem 157: Solving the diophantine equation | 5 | 301788 | problem-157-solving-the-diophantine-equation |
--description--
Consider the diophantine equation 1/a+1/b= p/10n with a, b, p, n positive integers and a ≤ b.
For n=1 this equation has 20 solutions that are listed below:
1/1+1/1=20/10
1/1+1/2=15/10
1/1+1/5=12/10
1/1+1/10=11/10
1/2+1/2=10/10
1/2+1/5=7/10
1/2+1/10=6/10
1/3+1/6=5/10
1/3+1/15=4/10
1/4+1/4=5/10
1/4+1/20=3/10
1/5+1/5=4/10
1/5+1/10=3/10
1/6+1/30=2/10
1/10+1/10=2/10
1/11+1/110=1/10
1/12+1/60=1/10
1/14+1/35=1/10
1/15+1/30=1/10
1/20+1/20=1/10
How many solutions has this equation for 1 ≤ n ≤ 9?
--hints--
euler157()
should return 53490.
assert.strictEqual(euler157(), 53490);
--seed--
--seed-contents--
function euler157() {
return true;
}
euler157();
--solutions--
// solution required