2022 · Q22
Let p = 2²ⁿ ⁺ ² + m and q = 2⁴ⁿ - m (where n is even natural number). What should be the least value of m such that p as well as q is divisible by 5?
Elementary MathematicsNumber System
- A-1
- B1
- C4
- D6
Explanation
For even n, 2^(2n+2) ≡ 4 (mod 5) and 2^(4n) ≡ 1 (mod 5), because 2⁴ ≡ 1 (mod 5). Then p ≡ 0 needs m ≡ 1 and q ≡ 0 also needs m ≡ 1. The least value among the options is 1. Hence the keyed option is B.