query: Divisibility rule for 7
positive_passages.docid: 11500
positive_passages.text: Divisibility by 7 rule, and Congruence Arithmetic Laws
negative_passages.docid: 90806
negative_passages.text: Find all positive integers $n$ such that $n$ is divisible by all the positive integers less than or equal to $\sqrt{n}$
negative_passages.docid: 100613
negative_passages.text: Prove that if an average of a thousand numbers is less than 7, then at least one of the numbers being averaged is less than 7
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: 117380
negative_passages.text: Divisibility Rule for 9
negative_passages.docid: 35666
negative_passages.text: How to prove the divisibility rule for $3\, $ [casting out threes]
negative_passages.docid: 24053
negative_passages.text: How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
negative_passages.docid: 27850
negative_passages.text: Find and prove a formula for $1\pmod{3}\cap 1\pmod{7}$.
negative_passages.docid: 50940
negative_passages.text: Prove $1^{2007}+2^{2007}+\cdots+n^{2007}$ is not divisible by $n+2$
negative_passages.docid: 27428
negative_passages.text: Divisibility test for $4$
negative_passages.docid: 32653
negative_passages.text: Smallest integer divisible by all up to $n$
negative_passages.docid: 132175
negative_passages.text: How many $5$-digit numbers with distinct digits are divisible by 3 (and generalize)
negative_passages.docid: 7473
negative_passages.text: How am I supposed to tell if a number is divisible by $13$ (I need a shortcut)?
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: 102265
negative_passages.text: Probability of 1x six from seven dice?
negative_passages.docid: 26614
negative_passages.text: Fermat: Last two digits of $7^{355}$
negative_passages.docid: 150430
negative_passages.text: Let $S={1, 2, 3, 4, ....., 2070}$ find the number of subsets of $S$ whose sum of elements in $S$ is divisible by 9