Question Number 101891 by bobhans last updated on 05/Jul/20

if x a integer number , when divided 8 has remainder 5 and divided 5 has remainder 2. find x

Answered by Rasheed.Sindhi last updated on 05/Jul/20

8−5=5−2=3 LCM(8,5)−3=40−3=37★

Commented byRasheed.Sindhi last updated on 05/Jul/20

This approach works when the difference of each divisor and its remainder is same. (lcm of divisors)−(diff. of divisor and remainder)

Commented bybemath last updated on 06/Jul/20

great sir

Answered by john santu last updated on 05/Jul/20

⇔x = 8p+5 ...(×5) ⇔x = 5q+2... (×8) ___________ − −3x = 40(p−q)+9 3x = 40(q−p)−9 x = ((40(q−p))/3) −3 q−p must be 3k , k∈Z (1)q−p=3 ⇔x = 37 (2)q−p=6 ⇔x= 77 (3)q−p=9⇔x=117 (4)q−p=12⇔x=157 and so on (JS ⊛)

Answered by floor(10²Eta[1]) last updated on 22/Jul/20

x≡5(mod 8)⇒x=5+8y, y∈Z x≡2(mod 5)⇒5+8y≡2(mod 5) ⇒8y≡2(mod 5), gcd(8,5)=1 ⇒4y≡1≡−4(mod 5), gcd(4, −4)=4∤5 ⇒y≡−1≡4(mod 5)⇒y=5z+4, z∈Z x=5+8(5z+4)=40z+37 x∈(37, 77,117, ...)∪(−3, −43,...)