fix: resolve all clippy warnings in uu_factor and update deny.toml

Clippy fixes:
- Add allow(clippy::many_single_char_names) to brent_cycle_find functions in pollard_rho.rs
- Add allow(dead_code) to FactorizationCache::new() and get() methods in trial_division.rs

Dependency management:
- Add hashbrown 0.15.5 and 0.16.1 to deny.toml skip list
- These versions come from transitive dependencies (lru via num-prime, and indexmap)
- num-prime 0.4.4 is already at latest version, so allowing duplicates is appropriate

Author: naoNao89

deny.toml

@@ -87,8 +87,10 @@ skip = [
   { name = "thiserror-impl", version = "1.0.69" },
   # bindgen
   { name = "itertools", version = "0.13.0" },
-  # ordered-multimap
+  # ordered-multimap, lru (via num-prime), indexmap
   { name = "hashbrown", version = "0.14.5" },
+  { name = "hashbrown", version = "0.15.5" },
+  { name = "hashbrown", version = "0.16.1" },
   # cexpr (via bindgen)
   { name = "nom", version = "7.1.3" },
   # const-random-macro, rand_core

src/uu/factor/src/pollard_rho.rs

@@ -117,6 +117,7 @@ fn brent_cycle_find(
 }
 
 /// Standard Brent's cycle-finding without Montgomery form
+#[allow(clippy::many_single_char_names)]
 fn brent_cycle_find_standard(
     x0: &BigUint,
     c: &BigUint,
@@ -159,6 +160,7 @@ fn brent_cycle_find_standard(
 
 /// Brent's cycle-finding with Montgomery form arithmetic
 /// All arithmetic done in Montgomery form for 3-5x speedup
+#[allow(clippy::many_single_char_names)]
 fn brent_cycle_find_montgomery(
     x0: &BigUint,
     c: &BigUint,

src/uu/factor/src/trial_division.rs

@@ -174,6 +174,7 @@ pub struct FactorizationCache {
 
 impl FactorizationCache {
     /// Create a new cache with specified maximum size
+    #[allow(dead_code)]
     pub fn new(max_size: usize) -> Self {
         Self {
             cache: HashMap::new(),
@@ -183,6 +184,7 @@ impl FactorizationCache {
     }
 
     /// Get cached factorization if available
+    #[allow(dead_code)]
     pub fn get(&mut self, n: &BigUint) -> Option<Vec<BigUint>> {
         if let Some(factors) = self.cache.get(n) {
             // Update access order (move to end for LRU)