I am reading the following paper:
http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.4233
It comes to the following claim: If $p$ is a prime number, and $Z$ is a multivariate polynomial, then:
$Z$ is zero modulo $p^{e+1}$ iff Z is zero modulo $P$ and $Z \choose p$ is zero modulo $p^e$ where $Z \choose p $ denotes the sum of all possible products of $p$ terms from $Z$ (we avoid using coefficients in writing $Z$ as sum of monomial terms, and repeat terms if necessary)
I fail to see why this is correct.
The "modulo P" is most likely a typo and they mean "modulo p", but P is used in the paper to describes polynomials, so maybe I'm missing something.
