Question

Exercitiul 3 .............................................

Answer 1

folosim teorema impartirii cu rest
x:15=c,  rest 13⇒    x=15c+13⇒    scadem termeni cu 13⇒
x:30=c,  rest 13⇒    x=30c+13
x:45=c,  rest 13⇒    x=45c+13


x-13=15c+13-13⇒    x-13=15c
x-13=30c+13-13⇒    x-13=30c
x-13=45c+13-13⇒    x-13=45c

x-13∈M15UM30UM45 deci x-13∈M[15,30,45]
[15,30,45]=2·3²·5=90
M90={0, 90, 180....}
daca x-13=90⇒  x=90+13⇒  x=103 deci cel mai mic nr.impartit la 15, 30, 45 sa dea rest 13 este nr.103