Geodesic
A greatest common divisor identity
The Teaching of Mathematics, XXI (2018) no. 2, p. 73
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In this paper, we present an identity involving the greatest common divisors of almost all possible subproducts of $n$ nonzero integers. Then we prove this identity, with the help of the fundamental theorem of arithmetic, and an identity concerning the minimum function $\min$. As a consequence, a new formula for the least common multiple is derived.
Classification : 97F60 F64
Keywords: Greatest common divisor, fundamental theorem of arithmetic, least common multiple. 
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     author = {Yuanhong Zhi},
     title = {A greatest common divisor identity},
     journal = {The Teaching of Mathematics},
     pages = {73 },
     year = {2018},
     volume = {XXI},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM2_2018_XXI_2_a1/}
}
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Yuanhong Zhi. A greatest common divisor identity. The Teaching of Mathematics, XXI (2018) no. 2, p. 73 . http://geodesic.mathdoc.fr/item/TM2_2018_XXI_2_a1/