query: Prove that $(x^n + y^n)$ is divisible by $(x + y)$ if $n$ is odd.
positive_passages.docid: 8366
positive_passages.text: Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
negative_passages.docid: 45037
negative_passages.text: Show $(2^m-1,2^n+1)=1$ if $m$ is odd
negative_passages.docid: 106847
negative_passages.text: Proof that $n^3+2n$ is divisible by $3$
negative_passages.docid: 82358
negative_passages.text: How to prove that $4^m + 5^m$ is divisible by 9 when m is an odd number
negative_passages.docid: 63416
negative_passages.text: Prove $(n^5-n)$ is divisible by 5 by induction.
negative_passages.docid: 103504
negative_passages.text: Weird $3^n$ in an identity to be combinatorially proved
negative_passages.docid: 13525
negative_passages.text: Prove: If $n=2^k-1$, then $\binom{n}{i}$ is odd for $0\leq i\leq n$
negative_passages.docid: 20626
negative_passages.text: Prove that $x^y < y^x$
negative_passages.docid: 10191
negative_passages.text: Binomial theorem: divisibility by $n^2$
negative_passages.docid: 35666
negative_passages.text: How to prove the divisibility rule for $3\, $ [casting out threes]
negative_passages.docid: 87665
negative_passages.text: Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
negative_passages.docid: 66578
negative_passages.text: Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
negative_passages.docid: 66016
negative_passages.text: Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
negative_passages.docid: 97411
negative_passages.text: If $x^n=y^n$ and $n$ is odd then $x=y$
negative_passages.docid: 77816
negative_passages.text: Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
negative_passages.docid: 98946
negative_passages.text: Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
negative_passages.docid: 142724
negative_passages.text: Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.