Question

Determinati cel mai mic numar natural genul care imp la 6,7 si 8 da respectiv resturile 5,6 si 8.
URGENTTT!!
DAU CORONIȚA CELUI CE RESPUNDE PRIMUL,IN MAX. 10 MINUTE!!!!!

Answer 1

n:6=c1 r5, n=6c1+5=6c1+6-1=6(c1+1)-1 ⇒ n+1=6(c1+1)
n:7=c2 r6, n=7c2+6=7c2+7-1=7(c2+1)-1 ⇒n+1=7(c2+1)
n:8=c3r7, n=8c3+7=8c3+8-1=8(c3+1)-1 ⇒ n+1=8(c3+1)

adica n+1 =M [6,7,8]=k*[6,7,8]
calculez [6,7,8]
6=2*3
7=7
8=2^3
[6,7,8]=2^3*3*7=168
pentru ca se cere cel mai mic nr ⇒ k=1
adica n+1=168
n=167