Given a positive integer $P>1$, let its prime factorization be written $$P=p\_1^{a\_1}p\_2^{a\_2}p\_3^{a\_3}\cdots p\_k^{a\_k}$$


Define the functions $h(P)$ by $h(1)=1$ and $h(P)=\min(a\_1, a\_2,\ldots,a\_k)$



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> Is the follows property true or false?
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> **The property**: *Let $n$ is a positive integer then $\min(h(n), h(n+1), h(n+2)) = 1$*
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**PS:** The property was checked up to $n=5.10^7$



Is min exponents of three positive integers $n$, $n+1$ and $n+2$ $=1$ true or false?
It is actually an old conjecture of **Erdős, Mollin, and Walsh** that the pattern you have noticed does indeed go on forever, i.e., there are no three consecutive [powerful numbers](https://en.wikipedia.org/wiki/Powerful_number).


