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Aflati numerele naturale prime a,b,c care verifica relatia: 3a+6b+5c=66.

Răspuns :

Nseara
3a+6b+5c=66 <=> a+2b+5c/3=22. => 3|5c => 3|c => c=3.
Deci 3a+6b+15=66 <=> 3a+6b=51 <=> a+2b=17.

b=2 => a=13, convine
b=3 => a=11, convine
b=5 => a=7, convine
b=7 => a=3, convine

Deci solutiile sunt: (a,b,c)={(13,2,3), (11,3,3), (7,5,3), (3,7,3)}.