Question

Determinati numarul de 3 cifre xyz ( cu bara ) scris in baza 10, care, impartit la rasturnatul sau zyx , sa dea catul 6 si restul 97

Answer 1

$xyz:zyx=6,rest97 \\ xyz=zyx*6+97 \\ xyz=(100z+10y+x)*6+97 \\ xyz=600z+60y+6x+97 \\ xyz-97=600z+60y+6x \\ (100x+10y+z)-97=600z+60y+6x \\ 100x+10y+z-600z+60y+6x=97 \\ 100x-6x+60y-10y+600z-z=97 \\ 94x+50y+599z=97 \\ =\ \textgreater \ xyz=743$