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x-2-mod-7-x-3-mod-4-x-

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Question Number 205922 by cortano12 last updated on 03/Apr/24
x = 2 (mod 7) x=3 (mod 4) x=?
x=2(mod7)x=3(mod4)x=?
Answered by Rasheed.Sindhi last updated on 03/Apr/24
x = 2 (mod 7) ∧ x=3 (mod 4) x=7m+2 ∧ 7m+2≡3(mod 4 ⇒7m≡1(mod 4 ⇒7m≡1+4∙5=21(mod 4 ⇒m≡3 ⇒x=7m+2=7(3)+2=23 ⇒x=23+lcm(7,4)×k ⇒x=23+28k ∀k∈Z
x=2(mod7)∧x=3(mod4)x=7m+2∧7m+2≡3(mod4⇒7m≡1(mod4⇒7m≡1+4⋅5=21(mod4⇒m≡3⇒x=7m+2=7(3)+2=23⇒x=23+lcm(7,4)×k⇒x=23+28k∀k∈Z
Answered by A5T last updated on 03/Apr/24
x=7k+2≡^4 3⇒3k≡^4 9⇒k≡^4 3⇒k=4q+3 ⇒x=7(4q+3)+2=28q+23
x=7k+2≡43⇒3k≡49⇒k≡43⇒k=4q+3⇒x=7(4q+3)+2=28q+23

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