CF 1372B - Omkar and Last Class of Math
The proposed solution does not answer the exercise that was asked. The exercise is: Compute the pseudo-quotient $q(x)$ and pseudo-remainder $r(x)$ for the given polynomials $u(x)$ and $v(x)$ over the integers.
CF 1372B - Omkar and Last Class of Math
Rating: 1300
Tags: greedy, math, number theory
Solve time: 1m 29s
Verified: no
Solution
Correctness
The proposed solution does not answer the exercise that was asked.
The exercise is:
Compute the pseudo-quotient $q(x)$ and pseudo-remainder $r(x)$ for the given polynomials $u(x)$ and $v(x)$ over the integers.
Instead of performing any polynomial pseudo-division, the proposed solution discusses an entirely different problem concerning $m$-survivors, prime-counting functions $\pi(x)$, and Exercise 4.5.4.41. It never defines the pseudo-division identity (1), never computes a pseudo-quotient, never computes a pseudo-remainder, and never uses the given polynomials $u(x)$ and $v(x)$.
Therefore it does not answer the question at all.
Gaps and Errors
- Critical error: The solution addresses a different exercise (the Lagarias-Miller-Odlyzko prime-counting exercise) instead of Exercise 4.6.1.1.
- Critical error: The given polynomials
$$u(x)=x^6+x^5-x^4+2x^3+3x^2-x+2$$
and
$$v(x)=2x^2+2x^2-x+3$$
are never used. 3. Critical error: No pseudo-division is carried out. 4. Critical error: Neither the pseudo-quotient $q(x)$ nor the pseudo-remainder $r(x)$ is computed. 5. Critical error: The defining pseudo-division relation is never stated or verified.
Summary
The submission is completely unrelated to the exercise being asked. Since it does not attempt the polynomial pseudo-division problem and provides neither $q(x)$ nor $r(x)$, it fails to answer the question.
VERDICT: FAIL - the proposed solution addresses an entirely different exercise and does not compute the required pseudo-quotient or pseudo-remainder.