2025 · Q20
Let p and q be two natural numbers such that (p+q)^(p+q) is divisible by 512. What is the least value of (p+q)?
Elementary MathematicsNumber System
- A4
- B6
- C8
- D12
Explanation
(p+q)^(p+q) divisible by 512=2^9 needs p+q even (else the power is odd). p+q=4: 4^4=256, no; p+q=6: 6^6=2^6*3^6, only 2^6, no; p+q=8: 8^8=2^24, yes. Least is 8. Checking p+q=6 carefully (2^6<2^9) avoids the trap.