Remainder

Number Theory Level 3

Find the remainder when $10^{7}$ is divided by 2003.

2^{8}

2^{11}

2^{10}

2^{9}

1 solution

Chew-Seong Cheong
Aug 30, 2017

$\begin{aligned} 10^7 & \equiv 1000(10000) \text{ (mod 2003)} \\ & \equiv 1000(5)(2003-3) \text{ (mod 2003)} \\ & \equiv -15000 \text{ (mod 2003)} \\ & \equiv -979 \text{ (mod 2003)} \\ & \equiv 1024 \text{ (mod 2003)} \\ & \equiv \boxed{2^{10}} \text{ (mod 2003)} \end{aligned}$

Remainder

1 solution

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