query: How to prove that $4^m + 5^m$ is divisible by 9 when m is an odd number
positive_passages.docid: 8366
positive_passages.text: Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
negative_passages.docid: 124685
negative_passages.text: How to show $(mn)!$ is divisible by $(m!)^n$?
negative_passages.docid: 115145
negative_passages.text: Show that $n-m$ is a multiple of 9 when $n$ and $m$ have same digits
negative_passages.docid: 87379
negative_passages.text: How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
negative_passages.docid: 35052
negative_passages.text: Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.
negative_passages.docid: 112031
negative_passages.text: Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
negative_passages.docid: 117380
negative_passages.text: Divisibility Rule for 9
negative_passages.docid: 146053
negative_passages.text: Proving identities (mod $pq$) using Fermat's little theorem?
negative_passages.docid: 148906
negative_passages.text: Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$
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: 109532
negative_passages.text: Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
negative_passages.docid: 103545
negative_passages.text: Prove "casting out nines" of an integer is equivalent to that integer modulo 9
negative_passages.docid: 69967
negative_passages.text: How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
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: 64668
negative_passages.text: Verify that $4(29!)+5!$ is divisible by $31$.
negative_passages.docid: 63416
negative_passages.text: Prove $(n^5-n)$ is divisible by 5 by induction.
negative_passages.docid: 103784
negative_passages.text: Show that $n^2+11n+2$ is not divisible by $113^2$ ( n is integer)