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,...)