HDU 4569 (推导)

Special equations

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 435    Accepted Submission(s): 274
Special Judge

Problem Description

　　Let f(x) = a _nx ⁿ +...+ a ₁x +a ₀, in which a _i (0 <= i <= n) are all known integers. We call f(x) 0 (mod m) congruence equation. If m is a composite, we can factor m into powers of primes and solve every such single equation after which we merge them using the Chinese Reminder Theorem. In this problem, you are asked to solve a much simpler version of such equations, with m to be prime's square.

 

Input

　　The first line is the number of equations T, T<=50.
　　Then comes T lines, each line starts with an integer deg (1<=deg<=4), meaning that f(x)'s degree is deg. Then follows deg integers, representing a _n to a ₀ (0 < abs(a _n) <= 100; abs(a _i) <= 10000 when deg >= 3, otherwise abs(a _i) <= 100000000, i 　　Remember, your task is to solve f(x) 0 (mod pri*pri)

 

Output

　　For each equation f(x) 0 (mod pri*pri), first output the case number, then output anyone of x if there are many x fitting the equation, else output "No solution!"

 

Sample Input

4 2 1 1 -5 7 1 5 -2995 9929 2 1 -96255532 8930 9811 4 14 5458 7754 4946 -2210 9601

 

Sample Output

Case #1: No solution! Case #2: 599 Case #3: 96255626 Case #4: No solution!

 

题意：求一个方程模m^2为0是否有解。

因为m是素数，所以方程模m^2为0必然需要方程模m为0，而所有的x(x>=m)模m为0，必

然有(x-m)模m为0.

所以就可以寻找[0,m-1]中f(x)模m为0的x，然后判断x+m,x+2m....是不是满足。

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