From 8a172e881d81f46cd07f331fddb58ef5260f55e3 Mon Sep 17 00:00:00 2001
From: jxu <7989982+jxu@users.noreply.github.com>
Date: Fri, 6 Jan 2023 09:38:37 -0500
Subject: [PATCH] Add note on pseudo-polynomial time
Resolves #985
---
src/algebra/factorization.md | 1 +
1 file changed, 1 insertion(+)
diff --git a/src/algebra/factorization.md b/src/algebra/factorization.md
index b879bad00..93d202cac 100644
--- a/src/algebra/factorization.md
+++ b/src/algebra/factorization.md
@@ -17,6 +17,7 @@ This is the most basic algorithm to find a prime factorization.
We divide by each possible divisor $d$.
We can notice, that it is impossible that all prime factors of a composite number $n$ are bigger than $\sqrt{n}$.
Therefore, we only need to test the divisors $2 \le d \le \sqrt{n}$, which gives us the prime factorization in $O(\sqrt{n})$.
+(This is [pseudo-polynomial time](https://en.wikipedia.org/wiki/Pseudo-polynomial_time), i.e. polynomial in the value of the input but exponential in the number of bits of the input.)
The smallest divisor has to be a prime number.
We remove the factor from the number, and repeat the process.
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