2018-10-10 22:03:03 +00:00
|
|
|
|
---
|
|
|
|
|
id: 5900f5071000cf542c510018
|
2020-12-16 07:37:30 +00:00
|
|
|
|
title: 问题410:圆和切线
|
2018-10-10 22:03:03 +00:00
|
|
|
|
challengeType: 5
|
|
|
|
|
videoUrl: ''
|
|
|
|
|
---
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --description--
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
设C为半径为r的圆,x2 + y2 = r2。我们选择两个点P(a,b)和Q(-a,c),使得穿过P和Q的线与C相切。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
例如,四元组(r,a,b,c)=(2,6,2,-7)满足该属性。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
令F(R,X)为具有该性质的整数四元组(r,a,b,c)的数量,并且0 <r≤R且0 <a≤X。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
我们可以验证F(1,5)= 10,F(2,10)= 52和F(10,100)= 3384.求F(108,109)+ F(109,108)。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --hints--
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`euler410()`应该返回799999783589946600。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
```js
|
2020-12-16 07:37:30 +00:00
|
|
|
|
assert.strictEqual(euler410(), 799999783589946600);
|
2018-10-10 22:03:03 +00:00
|
|
|
|
```
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --solutions--
|
2020-08-13 15:24:35 +00:00
|
|
|
|
|