Find X1 + x2 + X3 + X4 + x2010=x1·x2·x3·x4… ·Positive integer solutions of x2010 To process, wait online. Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! Urgent! 0 is not a positive integer, is to find all positive integer solutions

Let's say one in 2009, No,
Then suppose 2008 is 1
xy-x-y-2008=0
(x-1)(y-1)=2009=41*49=287*7=2009*1
therefore
x. Y = 42,50 or 288,8 or 2010,2
If it's a 1 in 2007, it will produce a fraction, no solution

X1, X2, X3,..., x2006 are integers
X1, X2, X3,..., x2006 are integers and - 1

The maximum is 2402 and the minimum is 200
The value ranges of x1, X2,..., x2006 are - 1,0,1,2. There are a, B, C and D values of - 1, 0, 1 and 2
Therefore, the original conditions are transformed into quaternion linear equations
a+b+c+d=2006（1）
-a+c+2d=200（2）
a+c+4d=2006（3）
Find the maximum and minimum of - A + C + 8D
From (1), (2), (3) we can see that:
b=3d, c=1103-3d, a=903-d
Using D to express - A + C + 8D, we get: 200 + 6D,
Then, the range of D is calculated
903-d > = 0 know: D = 0 know: D = 0
D min can be taken as 0, so the minimum value is 200
The maximum value of D is 367, so the maximum value is 2402

Let x1, X2, X3 X2006 is an integer and satisfies the following conditions;
① - 1 less than or equal to xn less than or equal to 2 n = 1,2,3 two thousand and six
②X1+X2+X3+… +X2006=200
③X1^2+X2^2+X3^2… +X2006^2=2006
Find X1 ^ 3 + x2 ^ 3 + X3 ^ 3 +Minimum and maximum values of x2006 ^ 3

Let x1, X2 In x2006, there are a 0, B - 1, C 1 and D 2
According to the meaning of the title, - B + C + 2D = 200
(-1)²b+1²c+2²d=2006 ②
① B + 3D = 1103
Ψ 0 ≤ D ≤ 367 (D means that the number cannot be negative or decimal)
x1³+x2³+...+x2006³=(-1)³b+1³c+2³d
=-b+c+8d ③
From (1) we get - B + C = 200-2d (4)
④ Substituting in (3)
x1³+x2³+...+x2006³=6d+200
When d = 0, there is a minimum value of 200
When d = 367, the maximum value is 2402

X1, X2, X3,..., x2006 are integers X1, X2, X3,..., x2006 are integers and - 1

Let x1, X2, X3 X2006 is an integer and satisfies the following conditions; ① - 1 less than or equal to xn less than or equal to 2 n = 1,2,3 two thousand and six ②X1+X2+X3+… +X2006=200 ③X1^2+X2^2+X3^2… +X2006^2=2006 Find X1 ^ 3 + x2 ^ 3 + X3 ^ 3 +Minimum and maximum values of x2006 ^ 3

RELATED INFORMATIONS

X1, X2, X3,..., x2006 are integers
X1, X2, X3,..., x2006 are integers and - 1

Let x1, X2, X3 X2006 is an integer and satisfies the following conditions;
① - 1 less than or equal to xn less than or equal to 2 n = 1,2,3 two thousand and six
②X1+X2+X3+… +X2006=200
③X1^2+X2^2+X3^2… +X2006^2=2006
Find X1 ^ 3 + x2 ^ 3 + X3 ^ 3 +Minimum and maximum values of x2006 ^ 3