Question

determinați nr. prime a.b.c stiind ca 6a+2b+9c=99

Answer 1

2b + 6a + 9c = 99
Cum 6a,9c,99 divizibil cu 3 => 2b divizibil cu 3 => cum (2,3) = 1 si b = prim => b = 3
6 + 6a + 9c = 99
6a + 9c = 99 - 6 = 93
3(2a + 3c) = 93
2a + 3c = 93 : 3 = 31
a = 2 => 3c = 31 - 4 = 27 => c = 27 : 3 = 9 (F)
a = 3 => 3c = 31 - 6 = 25, 25 nedivizibil cu 3(F)
a = 5 => 3c = 31 - 10 = 21 => c = 21 : 3 = 7
a = 7 => 3c = 31 - 14 = 17, nedivizibil cu 3 (F)
a = 11 => 3c = 31 - 22 = 9 => c = 9 : 3 = 3 
a = 13 => 3c = 31 - 26 = 5,nedivizibil cu 3 (F)
a = 17 => 3c = 31 - 34 (F)
a = 5, b = 3,c = 7 ; a = 11, b = 3, c = 3