Is CAP theorem wrong?

it helps some times Targeted towards the layman computer scientist:
The PCP theorem says that you can make proofs that are so easy to check that you only need to look at a constant number of (randomly selected) bits to (usually) tell a bad proof from a good one.

Any of those help Z3 has a new solver (nlsat) for nonlinear arithmetic. It is more efficient than other solvers (see this article). The new solver is complete for quantifier-free problems. However, the new solver does not support proof generation. If we disable proof generation, then Z3 will use nlsat and easily solve the problem. Based on your question, it seems you are really looking for solutions, thus disabling proof generation does not seem to be an issue.
Moreover, Z3 does not produce approximate solutions (like hand calculators). It uses a precise representation for real algebraic numbers. We can also ask Z3 to display the result in decimal notation (option :pp-decimal). Here is your example online.

(root-obj (+ (^ x 2) (- 2)) 1)

(- 1.4142135623?)

(set-option :pp-decimal true)
(declare-const a Real)
(declare-const b Real)
(declare-const c Real)
(assert (= a 1.0))
(assert (= b 1.0))
(assert (> c 0))
(assert (= (+ (* a a) (* b b)) (* c c)))
(check-sat)
(get-model)

(set-option :pp-decimal true)
(declare-const a Real)
(declare-const b Real)
(declare-const c Real)
(assert (> c 0))
(assert (> a c))
(assert (= (+ (* a a) (* b b)) (* c c)))
(check-sat)

this one helps. 0! = 1 by convention. Not 0. This might cause problem to you.
Moreover, for loop should go from 0 to n, not from 1 to n as there are n+1 terms.

for(int i = 0; i <= n; i++) {

    int product = 0;

    coefficient = factorial(n) / (factorial(i) * factorial(n - i));
    product = (int) (coefficient*Math.pow(a, n - i)*Math.pow(b, i));

    products.add(product);
}

I wish did fix the issue. Second version because it does not have a constrain on f(n).
As you see, in the first version your f(n) can be only in a specific form, the second case f(n) is any function, so you can solve recurrences like T(n) = 2 T(n/2) + nlog(n) + n^2 * sin(n)

will help you I am trying to check convolution theorem in MATLAB. I have a signal called sine_big_T. Then I have a filter called W. W and sine_big_T have the same length. , Using conv with 'same' is correct. You are seeing two things:

test = ifftshift( conv( fftshift(I_fft), fftshift(W_fft), 'same' ) );

plot(1:129,fft(sine_big_T.*W)*length(W));