Răspuns :
[tex]\displaystyle\bf\\\overline{ab} : (a + b) = 6~rest~2\\\overline{ba} : (a + b) = 4~rest~12\\..........\\(10a+b) : (a + b) = 6~rest~2\\(10b+a) : (a + b) = 4~rest~12\\..........\\10a+b = 6(a + b)+2\\10b+a = 4(a + b)+12\\..........\\10a+b = 6a + 6b+2\\10b+a = 4a + 4b+12\\..........\\10a-6a+b-6b=2\\10b-4b+a-4a=12\\..........\\4a-5b=2\\-3a+6b=12~~~\Big|:3\\..........\\4a-5b=2\\-a+2b=4\\\implies~a = -(4-2b)\\~~~~~~~~~\boxed{\bf a = 2b - 4}~~(Substitutie)\\[/tex]
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[tex]\displaystyle\bf\\4(2b - 4)-5b=2\\8b-16-5b=2\\8b-5b=2+16\\3b = 18\\b=18 : 3\\\boxed{\bf b = 6}\\Revenim~la~substitutie:\\a=2b-4\\a=2\times6-4\\a=12-4\\\boxed{\bf a=8}[/tex]
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Numarul este 86
Verificare:
86 : (8 + 6) = 86 : 14 = 6 rest 2
68 : (8 + 6) = 68 : 14 = 4 rest 12