query: Partition of Naturals in Arithmetic Progression
positive_passages.docid: 135955
positive_passages.text: Prove: The positive integers cannot be partitioned into arithmetic sequences (using Complex Analysis)
negative_passages.docid: 148239
negative_passages.text: natural deduction proof with De Morgan's laws
negative_passages.docid: 28496
negative_passages.text: Generating the partitions of a number
negative_passages.docid: 95373
negative_passages.text: Additive set function on a semiring of sets
negative_passages.docid: 28453
negative_passages.text: Finding all partitions of a set
negative_passages.docid: 107614
negative_passages.text: Partitioning an infinite set
negative_passages.docid: 43845
negative_passages.text: Partitioning the edges of $K_n$ into $\lfloor \frac n6 \rfloor$ planar subgraphs
negative_passages.docid: 46036
negative_passages.text: Logic for decomposing a permutation into different products composed of transpositions
negative_passages.docid: 65764
negative_passages.text: Partitioning $\{1,2,\ldots,k\}$ into $p$ subsets with equal sums, where $p$ is prime
negative_passages.docid: 8255
negative_passages.text: Real polynomials from repunits to repunits ( Putnam 2007 A4)
negative_passages.docid: 148260
negative_passages.text: Polylogarithms of negative integer order
negative_passages.docid: 37783
negative_passages.text: Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
negative_passages.docid: 56646
negative_passages.text: Arithmetic progression topology
negative_passages.docid: 39771
negative_passages.text: Is the natural log of n rational?
negative_passages.docid: 98618
negative_passages.text: Integer partition with fixed number of summands but without order
negative_passages.docid: 127678
negative_passages.text: A partition of the unit interval into uncountably many dense uncountable subsets
negative_passages.docid: 117862
negative_passages.text: Number of partitions of an $n$-element set into $k$ classes