x-4-mod-5-x-3-mod-4-

Question Number 134267 by bramlexs22 last updated on 01/Mar/21

{\begin{cases} x \equiv 4 (\mod 5) \\ x \equiv 3 (\mod 4) \end{cases}

Answered by EDWIN88 last updated on 01/Mar/21

{\begin{cases} x = 5 k + 4 \\ x = 4 ℓ + 3 \end{cases} \Leftrightarrow 5 k + 4 = 4 ℓ + 3

ℓ = \frac{5 k + 1}{4}; (k, ℓ) = (3, 4), (7, 9), (11, 14), \dots,

(4 λ - 1, 5 λ - 1) \Rightarrow then x = 5 (4 λ - 1) + 4

x = 20 λ - 1, λ \in Z = 19, 39, 59, 79, \dots

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