A9031. Pythagorean Theorem II
编程题
普及/提高-
知识点
题目描述
In mathematics, the Pythagorean theorem — is a relation in Euclidean geometry among the three sides of a right-angled triangle. In terms of areas, it states:
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides $a$ , $b$ and $c$ , often called the Pythagorean equation:
$a^{2}+b^{2}=c^{2}$ where $c$ represents the length of the hypotenuse, and $a$ and $b$ represent the lengths of the other two sides.
Given $n$ , your task is to count how many right-angled triangles with side-lengths $a$ , $b$ and $c$ that satisfied an inequality $1<=a<=b<=c<=n$ .
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides $a$ , $b$ and $c$ , often called the Pythagorean equation:
$a^{2}+b^{2}=c^{2}$ where $c$ represents the length of the hypotenuse, and $a$ and $b$ represent the lengths of the other two sides.
Given $n$ , your task is to count how many right-angled triangles with side-lengths $a$ , $b$ and $c$ that satisfied an inequality $1<=a<=b<=c<=n$ .
输入格式
The only line contains one integer $n (1<=n<=10^{4})$ as we mentioned above.
输出格式
Print a single integer — the answer to the problem.
输入输出样例
输入 #1
5
输出 #1
1
输入 #2
74
输出 #2
35