Resturi
Resturi
Sa se determine cel mai mic numar natural care impartit pe rand la \( 12, 15 \) si \( 18 \) sa dea resturile \( 6, 9 \) si respectiv \( 12 \).
. A snake that slithers on the ground can only dream of flying through the air.
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Andi Brojbeanu
- Bernoulli
- Posts: 294
- Joined: Sun Mar 22, 2009 6:31 pm
- Location: Targoviste (Dambovita)
Notam cea mai mica valoare posibila a numarului cerut cu \( n \).
\( n=12C_1+6;
n=15C_2+9;
n=18C_3+12 \).
Adunand 6, obtinem:
\( n+6=12C_1+12=12(C_1+1);
n+6=15C_2+15=15(C_2+1);
n+6=18C_3+18=18(C_3+1); \).
Adica \( N+6 \) este c.m.m.m.c al numerelor \( 12; 15; 18 \). \( [12; 15; 18]=180 \)\( \Rightarrow \)\( n=180-6=174 \).
\( n=12C_1+6;
n=15C_2+9;
n=18C_3+12 \).
Adunand 6, obtinem:
\( n+6=12C_1+12=12(C_1+1);
n+6=15C_2+15=15(C_2+1);
n+6=18C_3+18=18(C_3+1); \).
Adica \( N+6 \) este c.m.m.m.c al numerelor \( 12; 15; 18 \). \( [12; 15; 18]=180 \)\( \Rightarrow \)\( n=180-6=174 \).