Any permutation can be only either even or odd.
89474
every permutation is either even or odd,but not both
17277
Why is Euler's Totient function always even?
48787
A number is a perfect square if and only if it has odd number of positive divisors
128834
Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
35648
How many permutations of the set n={1,2,3,3,3,4,4,5} are possible without any consecutive identical elements?
94570
Proof that every odd integer is a difference of two squares
103538
Partitions of $n$ into distinct odd and even parts proof
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
111966
The exact difference between a permutation and a substitution
6273
Is there a possibility to choose fairly from three items when every choice can only have 2 options
98313
Number of possible permutations of n1 1's, n2 2's, n3 3's, n4 4's such that no two adjacent elements are same?
91951
How do I check if an integer is even or odd?
24212
proving how many permutations exist.
114796
Direct proof that the product of odd integers is odd
27889
If the set of odd numbers is a subset of $\mathbb N$ then surely it is smaller than $\mathbb N$
55718
Is zero odd or even?
47223
Deriving even odd function expressions