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An $n$-digit number that is the sum of the $n$th powers of its digits is called an $n$-narcissistic number. For example:

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Let $x$, $y$, and $z$ be positive integers satisfying the equation

$x+2yz=xyz$

How many ordered triplet solutions $(x,y,z)$ exist which satisfy the above equation?

Find the number of integer solutions for $p$, $q$, and $r$ that satisfy the equation:

$\frac{1}{p^2} + \frac{1}{q^2} = \frac{1}{r^2}$

where there is no common integer factor greater than $1$ …

Consider the set of natural numbers $\N$. Divide this set into two subsets, $S_1$ and $S_2$, where $\{ S_1 \cup S_2 \} = \N$ and ...

Given that $\alpha \beta \gamma = 6$, find the value of $abc$ for $a, b, c, d$ are positive integers and coprime satisfy these conditions:

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