query: Prove that the difference of an integer and its reverse order is divisible by 9
positive_passages.docid: 153302
positive_passages.text: $9$ divides $n-r(n)$ where $r(n)$ is $n$ with its digits reversed
negative_passages.docid: 74523
negative_passages.text: Proof by Cases involving divisibility
negative_passages.docid: 3632
negative_passages.text: Basic number theory proofs
negative_passages.docid: 120309
negative_passages.text: Number Theory Inequality Proof
negative_passages.docid: 108746
negative_passages.text: Prove that there exist two integers such that i - j is divisible by n.
negative_passages.docid: 77070
negative_passages.text: Prove Euler's Theorem when the integers are not relatively prime
negative_passages.docid: 117761
negative_passages.text: When is $\binom{n}{k}$ divisible by $n$?
negative_passages.docid: 10744
negative_passages.text: Prove that a number is divisible by 3 iff the sum of its digits is divisible by 3
negative_passages.docid: 31292
negative_passages.text: Divisibility Proof with Induction - Stuck on Induction Step
negative_passages.docid: 121706
negative_passages.text: Show $\text{det}(A)$ is divisible by $2^{n-1}$
negative_passages.docid: 71789
negative_passages.text: Prove that the sum of digits of $(999...9)^{3}$ (cube of integer with $n$ digits $9$) is $18n$
negative_passages.docid: 157294
negative_passages.text: Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
negative_passages.docid: 139776
negative_passages.text: Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens)
negative_passages.docid: 68971
negative_passages.text: Elementary approach to proving that a group of order 9 is Abelian
negative_passages.docid: 30136
negative_passages.text: Proof that a Combination is an integer
negative_passages.docid: 113950
negative_passages.text: Formula for reversing digits of positive integer $n$
negative_passages.docid: 113980
negative_passages.text: Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product