From b0323052f75b0c924a689bf3a0ce0f77f6c96d0d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Aleksy=20Wr=C3=B3blewski?= <alewro8@st.amu.edu.pl>
Date: Wed, 30 May 2018 17:44:28 +0000
Subject: [PATCH] =?UTF-8?q?Prze=C5=9Blij=20pliki=20do=20''?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

python hw.py
---
 hw.py | 47 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 hw.py

diff --git a/hw.py b/hw.py
new file mode 100644
index 0000000..029b759
--- /dev/null
+++ b/hw.py
@@ -0,0 +1,47 @@
+from fractions import gcd
+class Modulo:
+    def __init__(self, n):
+        self.elems = list(range(n))
+        self.n = n
+        self.reversibles = self.get_reversibles()
+        self.idempotent = self.get_idempotent()
+        self.zero_divisors = self.get_zero_divisors()
+        self.nilpotent = self.get_nilpotent()
+    '''elementy odwracalne to te, ktorych nwd z n jest rowne 1'''
+    def get_reversibles(self): 
+        return list(filter(lambda x: gcd(x, self.n) == 1, self.elems))
+    
+    '''nie rozwazamy elementow odwracalnych ani liczby 0
+    #dzielnik zera nie moze byc elementem odwracalnym'''
+    def get_zero_divisors(self):
+        potential_zeros = [ elem for elem in self.elems if elem not in self.reversibles ][1:]
+        results = []
+        for elem in potential_zeros:
+            for elem2 in potential_zeros:
+                if (elem * elem2) % self.n == 0:
+                    results.append(elem)
+                    break
+        return list(results) 
+
+    def get_idempotent(self):
+        '''element idempotentny => a^2 przystaje do a'''
+        return list(filter(lambda x: x*x % self.n == x, self.elems))
+
+    def get_nilpotent(self):
+        '''jesli pierscien nie zawiera dzielnikow zera, to nie zawiera takze elementow
+        nilpotentnych; wystarczy sprawdzic wsrod dzielnikow zera '''
+        potential_nils = self.zero_divisors
+        phi = len(self.reversibles) #funkcja fi
+        results = [] 
+        for elem in potential_nils:
+            for i in range(1, phi+1):
+                if elem**i % self.n == 0:
+                    results.append(elem)
+                    break
+        return results    
+
+def main():
+    m = Modulo(int(input()))
+    print([m.reversibles, m.zero_divisors, m.nilpotent, m.idempotent])
+if __name__ == '__main__':
+    main()
-- 
2.20.1