Question

Give an example of three positive integers m, n, and r, and three integers a, b,...

Give an example of three positive integers m, n, and r, and three integers a, b, and c such that the GCD of m, n, and r is 1, but there is no simultaneous solution to

x ≡ a (mod m)

x ≡ b (mod n)

x ≡ c (mod r).

Remark: This is to highlight the necessity of “relatively prime” in the hypothesis of the Chinese Remainder Theorem.

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