Ta có:
abc¯¯¯¯¯¯¯:(a+b+c)=25abc¯:(a+b+c)=25
⇒abc¯¯¯¯¯¯¯=25(a+b+c)⇒abc¯=25(a+b+c)
⇒abc¯¯¯¯¯¯¯⋮25⇒⎡⎣⎢⎢⎢⎢⎢abc¯¯¯¯¯¯¯=a00¯¯¯¯¯¯¯¯abc¯¯¯¯¯¯¯=a25¯¯¯¯¯¯¯¯abc¯¯¯¯¯¯¯=a50¯¯¯¯¯¯¯¯abc¯¯¯¯¯¯¯=a75¯¯¯¯¯¯¯¯⇒abc¯⋮25⇒[abc¯=a00¯abc¯=a25¯abc¯=a50¯abc¯=a75¯
TH1:abc¯¯¯¯¯¯¯=a00¯¯¯¯¯¯¯¯abc¯=a00¯
⇒a00¯¯¯¯¯¯¯¯=25.a⇒a00¯=25.a
⇒100a=25.a⇒100a=25.a
⇒a=0⇒a=0, loại.
TH2:abc¯¯¯¯¯¯¯=a25¯¯¯¯¯¯¯¯abc¯=a25¯
⇒a25¯¯¯¯¯¯¯¯=25(a+b+c)=25(a+2+5)=25a+175⇒a25¯=25(a+b+c)=25(a+2+5)=25a+175
⇒100a+25=25a+175⇒100a+25=25a+175
⇒100a−25a=175−25⇒100a−25a=175−25
⇒75a=150⇒a=2⇒75a=150⇒a=2
⇒a=b=2⇒a=b=2, loại.
TH3:abc¯¯¯¯¯¯¯=a50¯¯¯¯¯¯¯¯abc¯=a50¯
⇒a50¯¯¯¯¯¯¯¯=25(a+5+0)=25(a+5)=25a+125⇒a50¯=25(a+5+0)=25(a+5)=25a+125
⇒100a+50=25a+125⇒100a+50=25a+125
⇒75a=75⇒a=1(TM)⇒75a=75⇒a=1(TM)
TH4:abc¯¯¯¯¯¯¯=a75¯¯¯¯¯¯¯¯abc¯=a75¯
⇒a75¯¯¯¯¯¯¯¯=25(a+7+5)=25a+300⇒a75¯=25(a+7+5)=25a+300
⇒100a+75=25a+300⇒100a+75=25a+300
⇒75a=225⇒a=3(TM)⇒75a=225⇒a=3(TM)
Vậy abc¯¯¯¯¯¯¯∈{150;375}
