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What is the remainder when 7¹⁰³ is divided by 25?

1. 20
2. 16
3. 18
4. 15

Correct answer: 18

Solution

7^2 = 49 = -1 (mod 25). So 7^102 = (7^2)^51 = (-1)^51 = -1 (mod 25), and 7^103 = -7 = -7+25 = 18 (mod 25).

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