The remainder, when (15^ 23 + 23^ 23 ) is divided by 19, is - Vidyadip

Question

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

✓

Answer

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

$= 2 [19^{23} + ^{23}C_2 · 19^{21} · 4^2 + .......... + ^{23}C_{22} · 19 · 4^{22}]$

$= 2 · 19 [19^{22} + ^{23}C_2 · 19^{20} · 4^2 + .........+ ^{23}C_{22} · 4^{22}]$

$\Rightarrow E$ is divisible by $19 \Rightarrow$ Remainder $= 0$

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