Question

Determinati cel mai mic nr nat care impartit pe rand la 5,6,8 da resturile3,4,6

Answer 1

 [tex] n=M_5+3 |\;+2\;\;\rightarrow\;n+2=M_5+5=M_5;\\ n=M_6+4 |\;+2\;\;\rightarrow\;n+2=M_6+6=M_6;\\ n=M_8+6 |\;+2\;\;\rightarrow\;n+2=M_8+8=M_8;\\ \Rightarrow\;\;n+2 \;=\;[5;6;8]=120\;;\;n=120-2=...[/tex]

Answer 2

x:5=c rest 3 ⇒ x=5c+3⇒    x+2=5c+3+2⇒ x+2=5x+5
x:6=c rest4⇒   x=6c+4⇒    x+2=6c+4+2⇒ x+2=6c+6
x:8=c rest 6⇒  x=8c+6⇒    x+2=8c+6+2⇒ x+2=8c+8

x+2∈M[5,6,8]
[5,6,8]=5x2³x3=15x8=120
M120={120,240,360....}

x+2=120
x=120-2
x=118
verificare
118:5=23 rest 3
118:6=19 rest 4
118:8=14 rest 6
 deci cel mai mic nr.care satisface conditia este nr.118