2026 · Q31
Let P = N^2 where N is an odd integer. What is the remainder when P is divided by 8?
Elementary MathematicsNumber System
- A1
- B3
- C5
- DCannot be determined due to insufficient data
Explanation
Write the odd integer as N=2k+1; then P=N²=4k(k+1)+1. Since k(k+1) is always even, 4k(k+1) is a multiple of 8, so P leaves remainder 1 on division by 8, option A. Checking odd values like 3²=9 or 5²=25 confirms the remainder is always 1, never 3 or 5.