# All Questions

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### Need to create a specific four variable Boolean function?

I need to create a Boolean function consisting of four inputs (a,b,c,d) that is 1 if no more than 2 of its inputs are 1. I have experienced great difficulty on this particular problem. If anyone ...
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### proof of Laurents extension theorem

I found this theorem of Laurents expansion theorem online, but there is one thing I do not understand. How can he just say that $\gamma$ is a union of two cicles? Does he make some kind of ...
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### What's the probability of rolling the same number twice with a pair of dice?

There are a number of questions similar to this, but I'm asking about rolling two dice twice, not one die two times. Or I guess you could think of it as 4 dice total, with each pair distinguishable. ...
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### “locally finiteness” in coproducts

just to be sure: in any category of modules (as opposed to e.g. complete modules) any element $x$ in the (infinite) coproduct $X=\oplus_{\lambda\in\Lambda} X_\lambda$ can be written as a finite sum of ...
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### Divisibility !?? wihout mathematical induction if possible PLZ …

Hello I need to prove if $n\, |\, (x-a)$ and $n \, | \, f(x)$ then $n \, | \, f(a)$. It is true if $\operatorname{deg}(f)=1$ or $2$, but what for greater degree of $f(x)$? I don't know how to ...
Prove that there are infinitely many integer solutions to the diophantine equation: $(x-y)^7 = x^3y^3$