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Find the polynomials f(x),\ g(x) such that:

\frac{1}{\pi}\int_0^{\frac{1}{2}} \frac{tf'(t)-6g(t)}{\sqrt{1-t^2}}\ dt=f(x)-g(x)+x

\frac{6}{\pi}\int_0^{\frac{1}{2}} \frac{8f(t)-5g'(t)}{\sqrt{1-t^2}}\ dt=2f(x)-3g(x)-x^2+2x.
Posted by: kunny
Prove that for any set of n integers , there is a subset of them whose sum is divisible by n .

(I have one solution,but I think there exist many for this one)
Posted by: Curtis74200 » Today, 1:34 pm
Let a,b,p and q be real numbers such that 0<a,b<1, p,q\geq 0 and p+q=1. Prove that
$a^{p}b^{q}...
Posted by: ivanbart-15 » Today, 1:25 pm
\lim_{n \to \infty} \frac{1^{1}+2^{2}+ 3^{3} +  \ldots + n^{n}}{n^{n}}
Posted by: Random_Variable » Today, 12:41 pm
Let x,y,z>0 such that x^2+yz\ge1, y^2+zx\ge1,z^2+xy\ge1.Prove that x+y+z\ge2
Posted by: eddy13579 » Today, 12:36 pm
Пусть M[x] равно числу несократимых дробей a/b таких что, a<=x и b<=x, где a и b - натуральные числа. Вычислите сумму...
Posted by: z1c2b3m4 » Today, 12:26 pm
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