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Find all triplets of natural numbers such that y is a prime number , y and 3 do not divide z , \(x^3 - y^3 =z^2\)

In India, everyday the morning train is overloaded with a lot of milk cans hanged on the windows as you can see above. The five persons named BHEEM, KABIR, TULSI ...

If \(w=e^{2\pi{i}/2015},\) find \[\sum_{k=1}^{2014}\frac{1}{1+w^k+w^{2k}}.\]

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For some positive reals satisfying \(\displaystyle{ \sum_{i=1}^{24} x_i=1}\), determine the maximum possible value of ...

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