diff --git a/src/algebra/factorization.md b/src/algebra/factorization.md index 11bf4049c..51f206482 100644 --- a/src/algebra/factorization.md +++ b/src/algebra/factorization.md @@ -160,7 +160,7 @@ By looking at the squares $a^2$ modulo a fixed small number, it can be observed ## Pollard's $p - 1$ method { data-toc-label="Pollard's method" } It is very likely that at least one factor of a number is $B$**-powersmooth** for small $B$. -$B$-powersmooth means that every prime power $d^k$ that divides $p-1$ is at most $B$. +$B$-powersmooth means that every prime power $d^k$ that divides $p-1$ is at most $B$. Formally, let $\mathrm{B} \geqslant 1$ and $n \geqslant 1$ with prime factorization $n = \prod {p_i}^{e_i},$ then $n$ is $\mathrm{B}$-powersmooth if, for all $i,$ ${p_i}^{e_i} \leqslant \mathrm{B}$. E.g. the prime factorization of $4817191$ is $1303 \cdot 3697$. And the factors are $31$-powersmooth and $16$-powersmooth respectably, because $1303 - 1 = 2 \cdot 3 \cdot 7 \cdot 31$ and $3697 - 1 = 2^4 \cdot 3 \cdot 7 \cdot 11$. In 1974 John Pollard invented a method to extracts $B$-powersmooth factors from a composite number.