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Equality of vectors

Fun problem

Inequality

largest value

Find all positive integers $m$ and $n$ such that $\frac{m^3}{m+n}$ and $\frac{n^3}{m+n}$ are both prime numbers.

Find the square root of $1 + a^2 + \sqrt{1 + a^2 + a^4}$

Homotopy equivalence of closed curves

Calculate the integral

Calculate the sum

Tough integral