Tianak5996 Tianak5996

03-03-2022
Mathematics

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We can find a system of congruences where x≡a (mod 4) x≡b (mod 5) where the solution is x≡7 (mod 20).

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LammettHash LammettHash

03-03-2022

If x ≡ 7 (mod 20), then

x ≡ 7 ≡ 27 ≡ 47 ≡ 67 ≡ 87 ≡ … (mod 20)

or equivalently, x = 7 + 20k for some integer k.

Taken mod 4, we have

x ≡ 7 + 20k ≡ 3 (mod 4)

and mod 5,

x ≡ 7 + 20k ≡ 2 (mod 5)

so that a = 3 and b = 2.

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