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- W210666191 abstract "The terminology and notation used in this paper are introduced in the following articles: [20], [16], [9], [14], [18], [1], [10], [13], [12], [15], [11], [17], [21], [6], [7], [2], [5], [3], [8], [4], and [19]. For simplicity, we follow the rules: x, y, z, w denote real numbers, a, b, c, d, e, f , g denote natural numbers, k, l, m, n, m1, n1 denote integers, and q denotes a rational number. The following propositions are true: (1) If y 6= 0, then ( y ) = x a y . (2) x2 = x · x and (−x)2 = x2. (3) (−x)2·a = x2·a and (−x)2·a+1 = −x2·a+1. (4) If x 6= 0, then x Z = x. (5) If x 0 and y 0 and d > 0 and x = y, then x = y. (6) x > max(y, z) iff x > y and x > z. (7) If x ¬ 0 and y z, then y − x z and y z + x. (8) If x ¬ 0 and y > z or x z + x and y − x > z. Let us consider a, b. Then gcd(a, b) is a natural number. Let us observe that the functor gcd(a, b) is commutative. Let us consider m, n. Then m gcdn is an integer. Let us observe that the functor m gcdn is commutative." @default.
- W210666191 created "2016-06-24" @default.
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- W210666191 date "2007-04-27" @default.
- W210666191 modified "2023-10-03" @default.
- W210666191 title "Chinese Remainder Theorem" @default.
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- W210666191 doi "https://doi.org/10.3840/07001211" @default.
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