Geodesic
On solving big systems of congruences
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 116-118

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Let $S$ be a finite set of positive integers such that almost all its elements are pairwise coprime. An algorithm is presented for finding all elements $s\in S$, such that $(s,s')>1$ for an element $s'\in S$, $s'\ne s$. The algorithm allows to reduce any system of polynomial congruences to a number of systems with coprime moduli.
Keywords: coprime base, gcd, merge gcd, gcd tree. 
@article{PDMA_2013_6_a51,
     author = {K. D. Zhukov and A. S. Rybakov},
     title = {On solving big systems of congruences},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {116--118},
     publisher = {mathdoc},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2013_6_a51/}
}
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K. D. Zhukov; A. S. Rybakov. On solving big systems of congruences. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 116-118. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a51/