Exercise 2.3.4 (First examples, part 4)

Find all integers that give the remainders 1 , 2 , 3 when divided by 3 , 4 , 5 respectively.

Answers

Proof. An integer x is a solution if

x ≡ 1 ( mod 3 ) , x ≡ 2 ( mod 4 ) , x ≡ 3 ( mod 5 ) ,

where 3 , 4 , 5 are relatively prime by pairs.

A solution is x 0 = − 2 , so the solutions are

x = − 2 + k 60 , k ∈ ℤ .

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2024-08-11 10:11
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