WMC 2018 Senior Problem 29

Number Theory Level 2

What is the remainder when 10 30 {10}^{30} is divided by 998 998 ?

26 8 60 938 2

Tiger Ang by Tiger Ang , 20, Malaysia

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1 solution

Jordan Cahn
Oct 17, 2018

Let ≡ 998 \equiv_{998} denote congruence modulo 998. 1 0 30 = 100 0 10 ≡ 2 10 m o d 998 = 1024 ≡ 26 m o d 998 \begin{aligned} 10^{30} &= 1000^{10} \\ &\equiv 2^{10} &\mod 998 \\ &= 1024 \\ &\equiv \boxed{26} &\mod 998 \end{aligned}

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