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Does there exist a real number $r$ with $1<r<2$ such that the sequence of positive integers ...

If equation below have solution, find sum of all possible $n\in\mathbb{N}$:

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For a $N^\text{th}$ polynomial which satisfy $f(i) = \dfrac1{\binom{N+1}i }$ for $i = 0,1,2,\ldots, N$, what is the sum of the possible outcomes ...

Find the value of $k$ that makes the equation

$\sqrt{\left|(p^4 + kp^2q^2 + q^4) + (4p^3q - 4pq^3)i\right|} = p^2 + q^2$

true for ...

$a,b \in \mathbb{R}, a>b>0$, Find the minimum of $\sqrt{2}a^3+\dfrac{3}{ab-b^2}$

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