Question

determinati numerele naturale prime a,b si care verifica egalitatea : a+38b+60c=198

Answer 1

38b, 60c si 198 sunt numere pare, deci si a este par
Cum a este prim, a=2
38b+60c = 196
2(19b+30c) = 196
19b+30c = 98
$30c\in\{0,30,60,90\}$
$c\in\{0,1,2,3\}$
$c~este~prim\Rightarrow c\in\{2,3\}$
$c=2\Rightarrow19b+60=98;~19b=38;~b=2~si~b~este~prim$
$c=3\Rightarrow19b+90=98;~19b=8~si~b\not\in\mathbb{N}$
$\boxed{a=b=c=2}$