query: proof that the sum of digits of natural number are divisible by 3 iff the number is
positive_passages.docid: 3128
positive_passages.text: Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens)
negative_passages.docid: 30136
negative_passages.text: Proof that a Combination is an integer
negative_passages.docid: 103347
negative_passages.text: combinatorial proof of summation
negative_passages.docid: 132175
negative_passages.text: How many $5$-digit numbers with distinct digits are divisible by 3 (and generalize)
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
negative_passages.docid: 43113
negative_passages.text: Whether the given number is divisible by 24?
negative_passages.docid: 52644
negative_passages.text: Prove $2^k+1$ divisible by 3 for odd K
negative_passages.docid: 122577
negative_passages.text: Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
negative_passages.docid: 113119
negative_passages.text: Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
negative_passages.docid: 5257
negative_passages.text: Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
negative_passages.docid: 71625
negative_passages.text: Divisibility question
negative_passages.docid: 49687
negative_passages.text: Show that the number 9 divides the number $ m$ if and only if the sum of the digits of the number $ m $ is divisible by 9.
negative_passages.docid: 108919
negative_passages.text: Numbers till 400 divisible by 2, 3, 5, 7
negative_passages.docid: 125210
negative_passages.text: proof: primitive pythagorean triple, a or b has to be divisible by 3
negative_passages.docid: 147140
negative_passages.text: Prove the divisibility test by $7,11,13$ for numbers more than six digits
negative_passages.docid: 22154
negative_passages.text: Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
negative_passages.docid: 49096
negative_passages.text: How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$