query: Represent Integer as sum of at least two consecutive postive Integers
positive_passages.docid: 28099
positive_passages.text: Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers.
negative_passages.docid: 122891
negative_passages.text: integer as sum of three binomials
negative_passages.docid: 150324
negative_passages.text: Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.
negative_passages.docid: 94923
negative_passages.text: Using the Pigeonhole Principle to show that $2$ of any $n+1$ numbers from $\{1,2,\ldots,2n\}$ sum to $2n+1$
negative_passages.docid: 113331
negative_passages.text: Number of ways a natural number can be written as sum of smaller natural number
negative_passages.docid: 151466
negative_passages.text: Series of consecutive numbers (different lengths)
negative_passages.docid: 129163
negative_passages.text: Showing that every positive integer can be represented in this form
negative_passages.docid: 93572
negative_passages.text: How to determine if $n (n \geq 2)$ given numbers can be summed up to a certain number?
negative_passages.docid: 43610
negative_passages.text: Limit inferior of the quotient of two consecutive primes
negative_passages.docid: 27069
negative_passages.text: sum of all positive integers less than $n$ and relatively prime to $n$
negative_passages.docid: 132644
negative_passages.text: Convert a Pair of Integers to a Integer, Optimally?
negative_passages.docid: 64052
negative_passages.text: Among any three consecutive positive integers one is a multiple of 3
negative_passages.docid: 65978
negative_passages.text: How many subsets does the set $\{1, 2, \dots , n\}$ have that contain no two consecutive integers if $1$ and $n$ also count as consecutive?
negative_passages.docid: 104603
negative_passages.text: Integer program in which at least one of three inequalities holds
negative_passages.docid: 4194
negative_passages.text: Which integers can be expressed as a sum of squares of two coprime integers?
negative_passages.docid: 99868
negative_passages.text: Sum(Partition(Binary String)) = $2^k$
negative_passages.docid: 91704
negative_passages.text: Convert integers to written numbers