Project ForgeDiscrete Mathematics
Number Theory & Modular Arithmetic
GATE 2016
Medium
The value of the expression 13⁹⁹(mod 17), in the range 0 to 16, is ____.
4
Explanation
By Fermat's Little Theorem, 13¹⁶≡1 (mod 17). 99 = 6×16+3, so 13⁹⁹≡13³ (mod 17). 13²=169=9×17+16, so 13²≡16≡−1 (mod 17). 13³≡13×(−1)=−13≡4 (mod 17).
Source: GATE CS 2016 (Session 2 / Set B) (2016)
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