整数三角形题目两则

问题1: 周长不大于n，边长为整数的三角形有多少个？

解法：

Function p(ByVal n As Long)'周长n的三角形的个数
If n Mod 2 Then n = n + 3
p = Round(n ^ 2 / 48)
End Function
Sub Main()
Dim i As Long, c
For i = 1 To 10 ^ 6
c = c + p(i)
Next
Debug.Print c
End Sub

返回：6944486111111111

问题2: 周长不大于n，边长为整数，并且至少有一个角为整数（以角度表示）的三角形有多少个？

解法：

Function gcd(ByVal a As Long, ByVal b As Long) As Long
If b = 0 Then gcd = a: Exit Function
gcd = gcd(b, a Mod b)
End Function
Sub main()
Dim p As Long, c As Long
p = 10 ^ 6
c = p \ 3 '等边三角形的个数
Dim m As Long, n As Long, k As Long
For n = 1 To Int((Sqr(4 * p + 1) - 3) / 4) + 1
For k = 1 To Int((Sqr(n * n + 2 * p) - 3 * n) / 2)
m = n + k
If gcd(m, n) = 1 Then
If (m - n) Mod 2 = 1 Then c = c + p \ (2 * m * (m + n))
If (m - n) Mod 3 > 0 Then c = c + p \ (m * (2 * m + 3 * n) + n * n) + p \ (5 * m * n + 2 * (m * m + n * n)) + p \ (3 * m * (m + n))
End If
Next
Next
Debug.Print c
End Sub

返回：3055201