Question

The remainder, when $({15}^{23}+{23}^{23})$ is divided by $19$, is

• A. $4$
• B. $17$
• C. $23$
• D. $0$

Answer 1

Answer: (D)

$0$

Given, $(15{)}^{23}+(23{)}^{23}$

$=(19-4{)}^{23}+(19+4{)}^{23}$

$\Rightarrow$ In bino expansion of above expression the term containing 19 well be cancelled

as they disable by 19 then remaining term are

$\Rightarrow (-4{)}^{23}+(4{)}^{23}=0$

Therefore the remainder is exactly zero .