Question

Suma numerelor prime a,b şi c care verifică relaţia 33a+51b+7c=1209 este:​

Answer 1

Răspuns: Ai în imagine rezolvarea

Explicație pas cu pas:

Answer 2

$\it a,\ b,\ c\ -\ numere\ prime\ \ \ \ \ \ (1)\\ \\ 33a+51b+7c=1209\ \ \ \ \ \ \ \ \ (2)\\ \\ 33a,\ 51b,\ 1209\in M_3 \stackrel{(2)}{\Longrightarrow} 7c\in M_3 \stackrel{(1)}{\Longrightarrow}\ c=3\\ \\ Acum, rela\c{\it t}ia\ (2)\ devine:\\ \\ 33a+51b+21=1209|_{-21} \Rightarrow 33a+51b=1188 \ \ \ \ \ (3)$

$\it 33a,\ 1188 \in M_{11} \stackrel{(3)}{\Longrightarrow}\ 51b\in M_{11}\stackrel{(1)}{\Longrightarrow} b=11\\ \\ Acum,\ rela\c{\it t}ia\ (3)\ devine:\\ \\ 33a+51\cdot11=1188|_{:11} \Rightarrow 3a+51=108|_{:3} \Rightarrow a+17=36|_{-17} \Rightarrow\\ \\ \Rightarrow a=19$

NUmerele cerute sunt: a=19,  b=11,  c=3 .