diff --git a/telethon/client/telegrambaseclient.py b/telethon/client/telegrambaseclient.py
index a7aec132..099324a8 100644
--- a/telethon/client/telegrambaseclient.py
+++ b/telethon/client/telegrambaseclient.py
@@ -271,7 +271,7 @@ class TelegramBaseClient(abc.ABC):
         """
         Connects to Telegram.
         """
-        had_auth = self.session.auth_key is not None
+        old_auth = self.session.auth_key
         await self._sender.connect(
             self.session.server_address, self.session.port)
 
@@ -280,7 +280,7 @@ class TelegramBaseClient(abc.ABC):
 
         self._updates_handle = self._loop.create_task(self._update_loop())
 
-        if not had_auth:
+        if old_auth != self._sender.state.auth_key:
             self.session.auth_key = self._sender.state.auth_key
             self.session.save()
 
diff --git a/telethon/crypto/authkey.py b/telethon/crypto/authkey.py
index 31d1fc9c..64f65407 100644
--- a/telethon/crypto/authkey.py
+++ b/telethon/crypto/authkey.py
@@ -38,3 +38,6 @@ class AuthKey:
 
         # Calculates the message key from the given data
         return int.from_bytes(sha1(data).digest()[4:20], 'little', signed=True)
+
+    def __eq__(self, other):
+        return isinstance(other, type(self)) and other.key == self.key