Question

Determinati nr.prime care verifica egalitatea 2a+7b+6c=78

Answer 1

2a+7b+6c=78
2a se divide cu 2
6c se divide cu 2
78 se divide cu 2
⇒7b se divide cu 2
dar 7 nu se divide cu 2⇒b se divide cu si b=par⇒b=2
2a+7x2+6c=78/-14
2a+6c=64/:2
a+3c=32
I
a=par  I a=2
a=primI
2+3c=32/-2
3c=30/:3
c=10 (fals)
II
c=prim
c=par⇒c=2
a+3x2=32/-6
a=26 (fals)
III
c=prim
c=impar⇒c=3,5,7
a+3x3=32/-9
a=23(adevarat)
a+3x5=32/-15
a=17(adevarat)
a+3x7=32/-21
a=11(adevarat)
Raspuns:(a,b,c)∈{(23,2,3),(17,2,5),(11,2,7)}