# Tagged Questions

For questions related to the Chinese Remainder Theorem and its applications.

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### Remainder modulo matrices.

Is it possible to have a consistent definition of $A\bmod_{left} B$ that respects matrix multiplication from left where $A$ and $B$ are two square matrices with non-negative entries? Is there a ...
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### Chinese Remainder Theorem Consequence 2 [duplicate]

The Chinese remainder theorem as stated in my textbook: If $a,b \in \Bbb Z$ such that $\gcd(a,b) = 1$ then for arbitrary $c,d \in \Bbb Z$ there exists an $x \in \Bbb Z$ with $x \equiv c\bmod a$ and ...
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### Bézout's Identity of polynomials?

Let $P=X^3−7X+6$, $Q = 2X^2+ 5X − 3$ and $R = X^2 − 9 ∈\mathbb Q[X]$. What are $S$ and $T ∈\mathbb Q[X]$ such that $PS + QT = R$? I have calculate the greatest common divisor of $P,Q,R$ are $(x+3)$, ...
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### Recreational math dealing with twin primes

This is kinda recreational math with a goal in mind of progressing further toward a proof of the twin prime conjecture. Consider this: We start with a random prime: $109$ $3*109=327$ $327 \equiv$...
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### Chinese Remainder Theorem with form I have not seen

One of my professors gave out a practice exam for a Discrete Mathematics test, and I'm having a little trouble with this problem: "Use the Chinese Remainder's Theorem to find ALL solutions to the ...