Question

13to power73+14to power3 is divided by 11 then what is the remainder.

Answer 1

$\frac{ {13}^{73} + {14}^{3} }{11}$
$\frac{ {(11 + 2)}^{73} + {(11 + 3)}^{3} }{11}$
$(11m + {2}^{73} + {3}^{3} ) \div 11$
${2}^{4} = 11 + 6$
$(11m + {2}^{4 \times 18 + 1} + 9) \div 11$
$(11n + 2 + 4 \times 18 + 9) \div 11$
$(11b + 6) \div 11$
therefore,the number is 6