Răspuns:
1. ( [tex]2^{60} + 3^{45} +5^{40}[/tex]) : ( [tex]4^{30} + 5^{50} +3^{45}[/tex]) =( [tex]4^{30} +3^{45} + 5^{40}[/tex]) : ([tex]4^{30} + 3^{45} + 5^{40}[/tex])= 1
2. a= [tex]2^{n} *3^{n}[/tex](2+[tex]3^{2}[/tex]) = [tex]2^{n} *3^{n}[/tex] *11 => a este div cu 11 pentru orice n
3. a+b+c =450 b=a+1 c= a+2
a+a+1+a+2= 450 3a= 450- 3= 447 a= 447 :3=149
a= 149 b= 150 c= 151
4. 6a+9b= 45 / : 3 => 2a +3b= 15
10b+15c= 60 /:5 => 2b +3c= 12 se aduna ambele ecuatii
=> 2a +3b+2b+3c=15+12 2a+5b +3c= 27
5. a+b= 100 a= bx4+15 se inlocuieste in suma
4b+15+b= 100 5b= 100-15 =85 => b=85 :5=17
b= 17 a= 4x17+15 = 68+15= 83 a= 83 sau a=100-17-83
