Problem:   Is there a polynomial $p(x)$ with integer coefficients such that    $p(2013)=1789$ and $p(1515)=1830$?   My attempt:  After ruling out polynomials of degree 1, 2 and 3, and with further inspection, it appeared to me that such a polynomial doesn't exist.   Is my below proof accurate?    Suppose that $p$ exists, and let   $q(x)=p(x)-1789$ and $s(x)=p(x)-1830$  then,  $q(2013)=0$ and $s(1515)=0$, so clearly,  $q(x)=(x-2013)f(x)$ and $s(x)=(x-1515)g(x)$,   for some polynomials $f$ and $g$ with integer coefficients.   Let $a$, $c$ and $d$ be the constant terms of $p$, $g$ and $f$, respectively, and observe that the constant terms of $s$ and $q$ are    $-1515c=a-1830 \ $  and  $-2013d=a-1789$, $ \ $ respectively. $  \ \ \ \  \ \   (*)$   Thus,   $a \equiv 1830 \equiv 315 \pmod{1515}$  and $a \equiv 1789 \pmod{2013}$.  But this system of congruence doesn't have a simultaneous solution (since $ \gcd(1515, 2013)\not\mid 1789-315$).  Hence, there's no integer value of $a$ that satisfies $(*)$, which is a contradiction. Therefore, $p$ doesn't exist.    If the above is correct, is there perhaps a more direct way of proving this?
Let $a,b,c$ be $3$ distinct integers, and let $P$ be a polynomial with integer coefficients.Show that in this case the conditions $$P(a)=b,P(b)=c,P(c)=a$$ cannot be satisfied simultaneously.  Any hint would be appreciated.
Is there a way to exclude other particle systems from the effects of a Wind effect? I have a scene with a number of particle systems. I'd like to have a separate wind effect for my main scene and another for an extra: an emitter + wind-effect to blow leaves into my scene. I can't find any way to exclude, so here I am. At the very worst, I can just render the main scene and then render the wind effect and composite it, but I figured I'd check first. I have this weird object (vascular tree) which is empty inside, but closed from the top and the bottom:  However, it is empty inside, which makes me unable to use boolean on a bigger object (I want to make a hole in an object through which this object will go through). So I thought I should fill it and then try to boolean. But, how do I fill it?  Thank you sincerely. How do I kill processes in Ubuntu? How do I kill all processes running by my own non-root account?  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