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If $p$ is prime, then it is $p$-smooth and $p$-rough because both inequalities are not strict. $k$-rough is thus not $k-1$-smooth.

Also, a link to http://planetmath.org/encyclopedia/Addition.html is spurious.

Parting words from the person who closed the correction:

If $p$ is prime, then it is $p$-smooth and $p$-rough because both inequalities are not strict. $k$-rough is thus not $k-1$-smooth.
Also, a link to http://planetmath.org/encyclopedia/Addition.html is spurious.
You're right on both counts.

**Status:**Accepted

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Error

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## Versions

(v1) by Incnis Mrsi 2010-04-03