n:45=c, rest 2⇒ n=45c+2 scadem ambii termeni cu 2⇒ n-2=45c+2-2
n:36=c, rest 2⇒ n=36c+2 ⇒ n-2=36c+2-2
n:54=c, rest 2⇒ n=54c+2 ⇒ n-2=54c+2-2⇒
n-2=45c
n-2=36c
n-2=54c⇒ n-2∈M[45,36,54]
45=3²·5
36=2²·3²
54=3³·²
[45,36,54]=3³·2²·5=540
M(540)={0,540, 1080, 1620, 2160, 2700...}
a) n-2=540⇒ n=540+2
n=542 este cel mai mic nr.
540:45=12 rest 2
540:36=15 rest 2
540:54=10 rest2
b) pt.1500<n<2600⇒
pt. n-2=1620 ⇒n=1620+2
n=1622
1622:45=36, rest 2
1622:36=45, rest 2
1622:54=30, rest 2
pt.n-2=2160⇒ n=2160+2
n=2162
2162:45=48, rest 2
2162:36=60, rest 2
2162:54=40, rest 2
nr.cuprinse intre 1500 si 2600 care impartite la 45, 36, 54 dau rest 2 sunt 1622 si 2162