Prove that any function can be written as the sum of an even function and an odd function.
74447
How do I divide a function into even and odd sections?
72054
Show that $\deg f$ is even when $n$ is odd.
142724
Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
154288
proof that Even powers of an odd function's taylor polynomial vanish
129680
Prove that $n$ is even.
75229
Can there be a function that's even and odd at the same time?
146152
Characterising functions $f$ that can be written as $f = g \circ g$?
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
44880
Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even.
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
3341
Find $\sum_{r=1}^{3n-1}{ (-1)^{r-1}r\over{3n \choose r}}$, if $n$ is even
83679
Writing a non symmetrical function as an even or odd function
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
53194
Prove : $p$(n│even number of ODD parts)=$p$(n│distinct parts ,number of ODD parts is even )
45392
Every natural number can be written as the sum of distinct Fibonacci numbers?
156564
Prove the identity $\sum_{{{\underset{k-even}{k=0}}}}^{n}{n \choose k}2^{k}=\frac{3^{n}+(-1)^{n}}{2}$