query: Natural numbers and linear combinations
positive_passages.docid: 29084
positive_passages.text: Largest integer that can't be represented as a non-negative linear combination of $m, n = mn - m - n$? Why?
negative_passages.docid: 68882
negative_passages.text: Path to Combinatorics Problem [$1.11$]
negative_passages.docid: 115954
negative_passages.text: how to find maximal linearly independent subsets
negative_passages.docid: 41052
negative_passages.text: The set of real numbers and power set of the natural numbers
negative_passages.docid: 141227
negative_passages.text: How to show the integers have same cardinality as the natural numbers?
negative_passages.docid: 57954
negative_passages.text: How many transitive relations on a set of $n$ elements?
negative_passages.docid: 63260
negative_passages.text: Matrices whose Linear Combinations are All Singular
negative_passages.docid: 89611
negative_passages.text: Combinations of selecting $n$ objects with $k$ different types
negative_passages.docid: 96585
negative_passages.text: Sums and permutation
negative_passages.docid: 24582
negative_passages.text: Is the set of sequences of natural numbers with trailing zeros countable?
negative_passages.docid: 9971
negative_passages.text: enumerative combinatorics,In how many ways (as a function of n) can one choose a composition α α of n
negative_passages.docid: 32350
negative_passages.text: Compilation of proofs for the summation of natural squares and cubes
negative_passages.docid: 52682
negative_passages.text: Is the power set of the natural numbers countable?
negative_passages.docid: 66216
negative_passages.text: Squares, Cubes and Prime numbers
negative_passages.docid: 48502
negative_passages.text: number of ordered pairs of integers $(x,y)$ satisfying the equation
negative_passages.docid: 30136
negative_passages.text: Proof that a Combination is an integer
negative_passages.docid: 93459
negative_passages.text: Number of permutations of unspecified length