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diff --git a/requests/sessions.py b/requests/sessions.py
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index a0a23ee..9a51f33 100644
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--- a/requests/sessions.py
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+++ b/requests/sessions.py
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@@ -18,7 +18,7 @@ from .cookies import (
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     cookiejar_from_dict, extract_cookies_to_jar, RequestsCookieJar, merge_cookies)
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 from .models import Request, PreparedRequest, DEFAULT_REDIRECT_LIMIT
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 from .hooks import default_hooks, dispatch_hook
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-from .utils import to_key_val_list, default_headers, to_native_string
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+from .utils import to_key_val_list, default_headers, to_native_string, DEFAULT_PORTS
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 from .exceptions import (
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     TooManyRedirects, InvalidSchema, ChunkedEncodingError, ContentDecodingError)
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 from .packages.urllib3._collections import RecentlyUsedContainer
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@@ -103,8 +103,17 @@ class SessionRedirectMixin(object):
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         if (old_parsed.scheme == 'http' and old_parsed.port in (80, None)
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                 and new_parsed.scheme == 'https' and new_parsed.port in (443, None)):
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             return False
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+
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+        # Handle default port usage corresponding to scheme.
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+        changed_port = old_parsed.port != new_parsed.port
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+        changed_scheme = old_parsed.scheme != new_parsed.scheme
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+        default_port = (DEFAULT_PORTS.get(old_parsed.scheme, None), None)
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+        if (not changed_scheme and old_parsed.port in default_port
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+                and new_parsed.port in default_port):
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+            return False
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+
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         # Standard case: root URI must match
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-        return old_parsed.port != new_parsed.port or old_parsed.scheme != new_parsed.scheme
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+        return changed_port or changed_scheme
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     def resolve_redirects(self, resp, req, stream=False, timeout=None,
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                           verify=True, cert=None, proxies=None):
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diff --git a/requests/utils.py b/requests/utils.py
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index 8fba62d..14c94bd 100644
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--- a/requests/utils.py
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+++ b/requests/utils.py
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@@ -37,6 +37,8 @@ NETRC_FILES = ('.netrc', '_netrc')
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 DEFAULT_CA_BUNDLE_PATH = certs.where()
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+DEFAULT_PORTS = {'http': 80, 'https': 443}
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+
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 def dict_to_sequence(d):
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     """Returns an internal sequence dictionary update."""
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diff --git a/test_requests.py b/test_requests.py
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index e19b436..b76d2a4 100755
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--- a/test_requests.py
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+++ b/test_requests.py
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@@ -1012,6 +1012,17 @@ class RequestsTestCase(unittest.TestCase):
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         s = requests.Session()
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         assert s.should_strip_auth('http://example.com:1234/foo', 'https://example.com:4321/bar')
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+    @pytest.mark.parametrize(
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+        'old_uri, new_uri', (
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+            ('https://example.com:443/foo', 'https://example.com/bar'),
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+            ('http://example.com:80/foo', 'http://example.com/bar'),
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+            ('https://example.com/foo', 'https://example.com:443/bar'),
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+            ('http://example.com/foo', 'http://example.com:80/bar')
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+        ))
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+    def test_should_strip_auth_default_port(self, old_uri, new_uri):
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+        s = requests.Session()
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+        assert not s.should_strip_auth(old_uri, new_uri)
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+
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     def test_manual_redirect_with_partial_body_read(self):
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         s = requests.Session()
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         r1 = s.get(httpbin('redirect/2'), allow_redirects=False, stream=True)