Question

O florareasa daca face buchete cu 3 flori ii raman 2 flori,daca pune in buchet 5 flori ii raman patru flori,iar daca pun cate 7 ii raman 6 flori.
Numarul minim de flori pe care-l are florareasa este...

Answer 1

n:3=a rest 2
n:5=b rest 4
n:7=c rest 6

n=3a+2
n=5b+4
n=7c+6

Adunam la toate 1.

n+1=3a+3=3(a+1) ⇒ (n+1) ∈ M₃

n+1=5b+5=5(b+1) ⇒ (n+1) ∈ M₅

n+1=7c+7=7(c+1) ⇒ (n+1) ∈ M₇


(n+1) ∈ M₃

(n+1) ∈ M₅

(n+1) ∈ M₇
   ↓
n+1=[3, 5, 7]

[3, 5, 7]=3·5·7=15·7=105

n+1=105
n=104

....................
Sa ai o zi placuta :)