Abstract
The Ndistinct prime numbers that make up a composite number M allow its bi-partitioning into pairs of two relatively prime factors. Each such pair defines a pair of conjugate representations. An example of such pairs of conjugate representations, each of which spans the M-dimensional space, are the kq representations, which are the most natural representations for periodic systems. Here, we emphasize their relevance to factorizations: the number of prime numbers that make up M relates directly to the number of conjugate pairs of kq representations. It is also shown how Schwinger's factorization procedure is used for reducing M-dimensional space into subspaces according to the prime numbers that make up M.
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