2023 · Q15
When every even power of every odd integer (greater than 1) is divided by 8, what is the remainder?
Elementary MathematicsNumber System
- A3
- B2
- C1
- DThe remainder is not necessarily 1.
Explanation
For odd n = 2m + 1, n² = 4m(m + 1) + 1, and m(m + 1) is always even, so n² ≡ 1 (mod 8). Every even power n^{2k} = (n²)^k ≡ 1^k = 1 (mod 8). The remainder is therefore always 1 (C).