$\text{ If }{7}^{103}\text{ is divided by }25,\text{ then the remainder is }$

$\begin{array}{r}\text{ We have, }{7}^{103}=7(49{)}^{51}=7(50-1{)}^{51}\\ =50k-7=50k-25+18\end{array}$

$\text{ So, remainder is }18\text{ . }$