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diff --git a/requests/sessions.py b/requests/sessions.py
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index a448bd8..d73d700 100644
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--- a/requests/sessions.py
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+++ b/requests/sessions.py
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@@ -19,7 +19,7 @@ from .cookies import (
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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 ._internal_utils import to_native_string
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-from .utils import to_key_val_list, default_headers
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+from .utils import to_key_val_list, default_headers, DEFAULT_PORTS
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 from .exceptions import (
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     TooManyRedirects, InvalidSchema, ChunkedEncodingError, ContentDecodingError)
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@@ -128,8 +128,17 @@ 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, yield_requests=False, **adapter_kwargs):
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diff --git a/requests/utils.py b/requests/utils.py
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index 0ce7fe1..04145c8 100644
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--- a/requests/utils.py
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+++ b/requests/utils.py
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@@ -38,6 +38,8 @@ 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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 if sys.platform == 'win32':
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     # provide a proxy_bypass version on Windows without DNS lookups
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diff --git a/tests/test_requests.py b/tests/test_requests.py
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index f46561e..f99fdaf 100644
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--- a/tests/test_requests.py
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+++ b/tests/test_requests.py
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@@ -1611,6 +1611,17 @@ class TestRequests:
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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, httpbin):
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         s = requests.Session()
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         r1 = s.get(httpbin('redirect/2'), allow_redirects=False, stream=True)