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Multiple choice general knowledge

What is the remainder if (19 raised to 15 - 15 raised to 19) is divided by 17?

  1. 0

  2. 1

  3. 2

  4. 15

  5. 16

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Modulo 17: 19 ≡ 2, so 19^15 ≡ 2^15. 15 ≡ -2, so 15^19 ≡ (-2)^19 = -2^19. Expression = 2^15 - (-2^19) = 2^15 + 2^19 = 2^15(1+2^4) = 2^15(17) ≡ 0 (mod 17).

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