# All Questions

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### Congruencies with different moduli

How can I solve x congruent 4 (mod 5) x congruent 9 (mod 7) If my answer needs to be mod 35??
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### Show that $deg(f\cdot g)=n+m$

I started learning about rings and I was asked to proof some claims. I don't understand how I may prove the last one. I have proven that if $f$ and $g$ are polynomials over some ring of polynomials, ...
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### Maximum negative value?

What is the maximum negative value known in mathematics? How can I reach that maximum negative value on StackOverFlow? Thank You.
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### Association, Commutation and Identity Elements on Binary Operations?

Is the following closed, associative or commutative? f(a, b) = (a+b)/2, where a, b ∈ Z. I found that it is not closed but I am not sure how to find whether or not it is associative (I was confused ...
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### how to proceed ? Have I correctly transform the question to an equation?

Amongst Teaching staff of ABC university the ratio of men and women is 5 to 2. Amongst the women three seventh are not married . If the number of married women teacher is 56 then the total number of ...
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### Which solution is the right one??

If we want to solve the equation $sec^2(x)$ for finding the all roots(real and complex), we have two ways: 1-Direct solving for $sec^2(x)=0$ 2-Or by convert the above equation to polynomial series as ...
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### Integrability vs. Estimate

Given a finite measure space $\mu:\Sigma\to\mathbb{R}_+$. Consider measurable functions $f:\Omega\to\mathbb{C}$ and $g:\Omega\to\mathbb{C}$. Then the equivalence holds: ...
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### Robinson arithmetic and its incompleteness

Wikipedia in Italian has a sketch-of-proof that Robinson arithmetic is not complete, since commutativity of addition is undecidable. The sketch of proof creates a model that adds two elements, $a$ and ...
Let $$f(x) \leq g(x), \forall\, x.\hspace{0.5cm} (1)$$ Moreover, considering the indefinite integrals $$\int f(x)\,dx= F(x) + C_1 \hbox{ and } \int g(x)\,dx = G(x) + C_2.$$ My question: If we ...
### Why is $\vec{s}=\frac{\vec{r}}{V^\frac{1}{3}} \Leftrightarrow d\vec{s}=\frac{d\vec{r}}{V}$?
I am following a course which contains a part in statistical thermodynamics. One of the questions involves the partition function $Q_N$. I could not figure out the answer of the question myself, so I ...