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What is the remainder when 2²⁰⁰³ is divided by 17?
- 1
- 2
- 8
- none of these
Correct answer: 8
Solution
By Fermat's little theorem, 2¹⁶ ≡ 1 (mod 17). Write 2003 = 16*125 + 3. Then 2²⁰⁰³ = (2¹⁶)¹²⁵ * 2³ ≡ 1¹²⁵ * 8 = 8 (mod 17). The remainder is 8.
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