diff --git a/doc/lispref/numbers.texi b/doc/lispref/numbers.texi
index fc52f11cf4a..ee43389399a 100644
--- a/doc/lispref/numbers.texi
+++ b/doc/lispref/numbers.texi
@@ -409,6 +409,16 @@ if so, @code{nil} otherwise.  The argument must be a number.
 @code{(zerop x)} is equivalent to @code{(= x 0)}.
 @end defun
 
+@defun oddp integer
+This predicate tests whether its argument is an odd number, and returns
+@code{t} if so, @code{nil} otherwise.  The argument must be an integer.
+@end defun
+
+@defun evenp integer
+This predicate tests whether its argument is an even number, and returns
+@code{t} if so, @code{nil} otherwise.  The argument must be an integer.
+@end defun
+
 @node Comparison of Numbers
 @section Comparison of Numbers
 @cindex number comparison
diff --git a/doc/misc/cl.texi b/doc/misc/cl.texi
index fbed1265aa3..f481f6f2721 100644
--- a/doc/misc/cl.texi
+++ b/doc/misc/cl.texi
@@ -2450,7 +2450,7 @@ by the name @code{it} in the ``then'' part.  For example:
 (setq funny-numbers '(6 13 -1))
      @result{} (6 13 -1)
 (cl-loop for x below 10
-         if (cl-oddp x)
+         if (oddp x)
            collect x into odds
            and if (memq x funny-numbers) return (cdr it) end
          else
@@ -3055,7 +3055,7 @@ This section defines a few simple Common Lisp operations on numbers
 that were left out of Emacs Lisp.
 
 @menu
-* Predicates on Numbers::       @code{cl-plusp}, @code{cl-oddp}, etc.
+* Predicates on Numbers::       @code{cl-plusp}, @code{cl-minusp}, etc.
 * Numerical Functions::         @code{cl-floor}, @code{cl-ceiling}, etc.
 * Random Numbers::              @code{cl-random}, @code{cl-make-random-state}.
 * Implementation Parameters::   @code{cl-most-positive-float}, etc.
@@ -3078,16 +3078,6 @@ This predicate tests whether @var{number} is negative.  It is an
 error if the argument is not a number.
 @end defun
 
-@defun cl-oddp integer
-This predicate tests whether @var{integer} is odd.  It is an
-error if the argument is not an integer.
-@end defun
-
-@defun cl-evenp integer
-This predicate tests whether @var{integer} is even.  It is an
-error if the argument is not an integer.
-@end defun
-
 @defun cl-digit-char-p char radix
 Test if @var{char} is a digit in the specified @var{radix} (default is
 10).  If it is, return the numerical value of digit @var{char} in
diff --git a/etc/NEWS b/etc/NEWS
index 6d934b2029c..a0d0f8b9818 100644
--- a/etc/NEWS
+++ b/etc/NEWS
@@ -1265,6 +1265,12 @@ restore the old behavior, you can set 'eshell-pwd-convert-function' to
 
 * Lisp Changes in Emacs 31.1
 
++++
+** New functions 'oddp' and 'evenp'.
+They return non-nil if an integer is odd or even, respectively, and
+signal an error if they are given a non-integer.  The 'cl-lib' functions
+'cl-oddp' and 'cl-evenp' are now aliases for 'oddp' and 'evenp'.
+
 ** Time & Date
 
 +++
diff --git a/lisp/emacs-lisp/cl-lib.el b/lisp/emacs-lisp/cl-lib.el
index dba01b28325..1fc36517796 100644
--- a/lisp/emacs-lisp/cl-lib.el
+++ b/lisp/emacs-lisp/cl-lib.el
@@ -280,17 +280,17 @@ so that they are registered at compile-time as well as run-time."
   (declare (side-effect-free t))
   (< number 0))
 
-(defun cl-oddp (integer)
-  "Return t if INTEGER is odd."
-  (declare (side-effect-free t)
-           (compiler-macro (lambda (_) `(eq (logand ,integer 1) 1))))
-  (eq (logand integer 1) 1))
+(defalias 'cl-oddp #'oddp
+  "Return t if INTEGER is odd.
 
-(defun cl-evenp (integer)
-  "Return t if INTEGER is even."
-  (declare (side-effect-free t)
-           (compiler-macro (lambda (_) `(eq (logand ,integer 1) 0))))
-  (eq (logand integer 1) 0))
+This function is considered deprecated in favor of the built-in function
+`evenp' that was added in Emacs 31.1.")
+
+(defalias 'cl-evenp #'evenp
+  "Return t if INTEGER is even.
+
+This function is considered deprecated in favor of the built-in function
+`evenp' that was added in Emacs 31.1.")
 
 (defconst cl-digit-char-table
   (let* ((digits (make-vector 256 nil))
diff --git a/lisp/emacs-lisp/shortdoc.el b/lisp/emacs-lisp/shortdoc.el
index cc9971b232f..af995123dc5 100644
--- a/lisp/emacs-lisp/shortdoc.el
+++ b/lisp/emacs-lisp/shortdoc.el
@@ -278,17 +278,17 @@ A FUNC form can have any number of `:no-eval' (or `:no-value'),
    :args (function map)
    :eval (map-values-apply #'1+ (list '(1 . 2)  '(3 . 4))))
   (map-filter
-   :eval (map-filter (lambda (k _) (cl-oddp k)) (list '(1 . 2) '(4 . 6)))
-   :eval (map-filter (lambda (k v) (cl-evenp (+ k v))) (list '(1 . 2) '(4 . 6))))
+   :eval (map-filter (lambda (k _) (oddp k)) (list '(1 . 2) '(4 . 6)))
+   :eval (map-filter (lambda (k v) (evenp (+ k v))) (list '(1 . 2) '(4 . 6))))
   (map-remove
-   :eval (map-remove (lambda (k _) (cl-oddp k)) (list '(1 . 2) '(4 . 6)))
-   :eval (map-remove (lambda (k v) (cl-evenp (+ k v))) (list '(1 . 2) '(4 . 6))))
+   :eval (map-remove (lambda (k _) (oddp k)) (list '(1 . 2) '(4 . 6)))
+   :eval (map-remove (lambda (k v) (evenp (+ k v))) (list '(1 . 2) '(4 . 6))))
   (map-some
-   :eval (map-some (lambda (k _) (cl-oddp k)) (list '(1 . 2) '(4 . 6)))
-   :eval (map-some (lambda (k v) (cl-evenp (+ k v))) (list '(1 . 2) '(4 . 6))))
+   :eval (map-some (lambda (k _) (oddp k)) (list '(1 . 2) '(4 . 6)))
+   :eval (map-some (lambda (k v) (evenp (+ k v))) (list '(1 . 2) '(4 . 6))))
   (map-every-p
-   :eval (map-every-p (lambda (k _) (cl-oddp k)) (list '(1 . 2) '(4 . 6)))
-   :eval (map-every-p (lambda (k v) (cl-evenp (+ k v))) (list '(1 . 3) '(4 . 6))))
+   :eval (map-every-p (lambda (k _) (oddp k)) (list '(1 . 2) '(4 . 6)))
+   :eval (map-every-p (lambda (k v) (evenp (+ k v))) (list '(1 . 3) '(4 . 6))))
   "Combining and changing maps"
   (map-merge
    :eval (map-merge 'alist '(1 2 3 4) #s(hash-table data (5 6 7 8)))
@@ -1418,10 +1418,10 @@ A FUNC form can have any number of `:no-eval' (or `:no-value'),
   (cl-minusp
    :eval (cl-minusp 0)
    :eval (cl-minusp -1))
-  (cl-oddp
-   :eval (cl-oddp 3))
-  (cl-evenp
-   :eval (cl-evenp 6))
+  (oddp
+   :eval (oddp 3))
+  (evenp
+   :eval (evenp 6))
   (bignump
    :eval (bignump 4)
    :eval (bignump (expt 2 90)))
diff --git a/lisp/obsolete/cl.el b/lisp/obsolete/cl.el
index 2ee7e70e4ea..4fb49b596e2 100644
--- a/lisp/obsolete/cl.el
+++ b/lisp/obsolete/cl.el
@@ -272,8 +272,6 @@
                first
                svref
                copy-seq
-               evenp
-               oddp
                minusp
                plusp
                floatp-safe
diff --git a/lisp/subr.el b/lisp/subr.el
index 77e909d1bf6..173c69675aa 100644
--- a/lisp/subr.el
+++ b/lisp/subr.el
@@ -550,6 +550,20 @@ was called."
            (compiler-macro (lambda (_) `(= 0 ,number))))
   (= 0 number))
 
+(defun oddp (integer)
+  "Return t if INTEGER is odd."
+  (declare (ftype (function (integer) boolean))
+           (side-effect-free t)
+           (compiler-macro (lambda (_) `(eq (logand ,integer 1) 1))))
+  (eq (logand integer 1) 1))
+
+(defun evenp (integer)
+  "Return t if INTEGER is even."
+  (declare (ftype (function (integer) boolean))
+           (side-effect-free t)
+           (compiler-macro (lambda (_) `(eq (logand ,integer 1) 0))))
+  (eq (logand integer 1) 0))
+
 (defun fixnump (object)
   "Return t if OBJECT is a fixnum."
   (declare (ftype (function (t) boolean))
diff --git a/test/lisp/emacs-lisp/cl-lib-tests.el b/test/lisp/emacs-lisp/cl-lib-tests.el
index 12de268bced..4121c1bfdb0 100644
--- a/test/lisp/emacs-lisp/cl-lib-tests.el
+++ b/test/lisp/emacs-lisp/cl-lib-tests.el
@@ -111,26 +111,6 @@
   (should-not (cl-minusp 1.0e+INF))
   (should-error (cl-minusp "-42") :type 'wrong-type-argument))
 
-(ert-deftest cl-lib-test-oddp ()
-  (should (cl-oddp -3))
-  (should (cl-oddp 3))
-  (should-not (cl-oddp -2))
-  (should-not (cl-oddp 0))
-  (should-not (cl-oddp 2))
-  (should-error (cl-oddp 3.0e+NaN) :type 'wrong-type-argument)
-  (should-error (cl-oddp 3.0) :type 'wrong-type-argument)
-  (should-error (cl-oddp "3") :type 'wrong-type-argument))
-
-(ert-deftest cl-lib-test-evenp ()
-  (should (cl-evenp -2))
-  (should (cl-evenp 0))
-  (should (cl-evenp 2))
-  (should-not (cl-evenp -3))
-  (should-not (cl-evenp 3))
-  (should-error (cl-evenp 2.0e+NaN) :type 'wrong-type-argument)
-  (should-error (cl-evenp 2.0) :type 'wrong-type-argument)
-  (should-error (cl-evenp "2") :type 'wrong-type-argument))
-
 (ert-deftest cl-digit-char-p ()
   (should (eql 3 (cl-digit-char-p ?3)))
   (should (eql 10 (cl-digit-char-p ?a 11)))
diff --git a/test/lisp/subr-tests.el b/test/lisp/subr-tests.el
index 29767ed07b5..1b209ab6383 100644
--- a/test/lisp/subr-tests.el
+++ b/test/lisp/subr-tests.el
@@ -45,6 +45,26 @@
   (should-not (zerop (1- most-negative-fixnum)))
   (should-error (zerop "-5") :type 'wrong-type-argument))
 
+(ert-deftest subr-test-oddp ()
+  (should (oddp -3))
+  (should (oddp 3))
+  (should-not (oddp -2))
+  (should-not (oddp 0))
+  (should-not (oddp 2))
+  (should-error (oddp 3.0e+NaN) :type 'wrong-type-argument)
+  (should-error (oddp 3.0) :type 'wrong-type-argument)
+  (should-error (oddp "3") :type 'wrong-type-argument))
+
+(ert-deftest subr-test-evenp ()
+  (should (evenp -2))
+  (should (evenp 0))
+  (should (evenp 2))
+  (should-not (evenp -3))
+  (should-not (evenp 3))
+  (should-error (evenp 2.0e+NaN) :type 'wrong-type-argument)
+  (should-error (evenp 2.0) :type 'wrong-type-argument)
+  (should-error (evenp "2") :type 'wrong-type-argument))
+
 (ert-deftest let-when-compile ()
   ;; good case
   (should (equal (macroexpand '(let-when-compile ((foo (+ 2 3)))