2025 · Q5
Let p be the remainder when 7⁸⁴ is divided by 342 and q be the remainder when 7⁸⁴ is divided by 344. What is (p – q) equal to ?
Elementary MathematicsNumber System
- A0
- B1
- C2
- D6
Explanation
Since 7³ = 343, modulo 342 we have 343 ≡ 1, so 7⁸⁴ = (7³)²⁸ ≡ 1²⁸ = 1 and p = 1. Modulo 344 we have 343 ≡ −1, so 7⁸⁴ = (7³)²⁸ ≡ (−1)²⁸ = 1 and q = 1. Therefore p − q = 1 − 1 = 0, option (a).