diff --git a/cryptography/hazmat/primitives/asymmetric/rsa.py b/cryptography/hazmat/primitives/asymmetric/rsa.py
index 9124757..1b33eaa 100644
--- a/cryptography/hazmat/primitives/asymmetric/rsa.py
+++ b/cryptography/hazmat/primitives/asymmetric/rsa.py
@@ -43,6 +43,9 @@
         if public_exponent < 3 or public_exponent >= modulus:
             raise ValueError("public_exponent must be >= 3 and < modulus")
 
+        if public_exponent & 1 == 0:
+            raise ValueError("public_exponent must be odd")
+
         self._public_exponent = public_exponent
         self._modulus = modulus
 
@@ -94,6 +97,9 @@
         if public_exponent < 3 or public_exponent >= modulus:
             raise ValueError("public_exponent must be >= 3 and < modulus")
 
+        if public_exponent & 1 == 0:
+            raise ValueError("public_exponent must be odd")
+
         if p * q != modulus:
             raise ValueError("p*q must equal modulus")
 
diff --git a/tests/hazmat/primitives/test_rsa.py b/tests/hazmat/primitives/test_rsa.py
index 50b3f7a..b89daac 100644
--- a/tests/hazmat/primitives/test_rsa.py
+++ b/tests/hazmat/primitives/test_rsa.py
@@ -69,46 +69,54 @@
 
     def test_invalid_argument_values(self):
         # tiny example key
-        rsa.RSAPrivateKey(3, 5, 14, 8, 15)
+        rsa.RSAPrivateKey(3, 5, 14, 7, 15)
 
         # modulus too small
         with pytest.raises(ValueError):
-            rsa.RSAPrivateKey(3, 5, 14, 8, 2)
+            rsa.RSAPrivateKey(3, 5, 14, 7, 2)
 
         # modulus wrong
         with pytest.raises(ValueError):
-            rsa.RSAPrivateKey(3, 5, 14, 8, 16)
+            rsa.RSAPrivateKey(3, 5, 14, 7, 16)
 
         # p too high
         with pytest.raises(ValueError):
-            rsa.RSAPrivateKey(16, 5, 14, 8, 15)
+            rsa.RSAPrivateKey(16, 5, 14, 7, 15)
 
         # q too high
         with pytest.raises(ValueError):
-            rsa.RSAPrivateKey(3, 16, 14, 8, 15)
+            rsa.RSAPrivateKey(3, 16, 14, 7, 15)
 
         # private exp too high
         with pytest.raises(ValueError):
-            rsa.RSAPrivateKey(3, 5, 16, 8, 15)
+            rsa.RSAPrivateKey(3, 5, 16, 7, 15)
 
         # public exp too low
         with pytest.raises(ValueError):
-            rsa.RSAPrivateKey(3, 5, 14, 2, 15)
+            rsa.RSAPrivateKey(3, 5, 14, 1, 15)
 
         # public exp too high
         with pytest.raises(ValueError):
-            rsa.RSAPrivateKey(3, 5, 14, 16, 15)
+            rsa.RSAPrivateKey(3, 5, 14, 17, 15)
 
-        rsa.RSAPublicKey(8, 15)
+        # public exp not odd
+        with pytest.raises(ValueError):
+            rsa.RSAPrivateKey(3, 5, 14, 8, 15)
+
+        rsa.RSAPublicKey(7, 15)
 
         # modulus too small
         with pytest.raises(ValueError):
-            rsa.RSAPublicKey(8, 2)
+            rsa.RSAPublicKey(7, 2)
 
         # public exp too low
         with pytest.raises(ValueError):
-            rsa.RSAPublicKey(2, 15)
+            rsa.RSAPublicKey(1, 15)
 
         # public exp too high
         with pytest.raises(ValueError):
-            rsa.RSAPublicKey(16, 15)
+            rsa.RSAPublicKey(17, 15)
+
+        # public exp not odd
+        with pytest.raises(ValueError):
+            rsa.RSAPublicKey(8, 15)