The least non-negative remainder when 3^2026 is divided by 13 is: Option 1: 9 Option 2: 7 Option 3: 1 Option 4: 3

Answer: 3. Solution: 3^3=271±od13, so the powers of 3 repeat with period 3. 2026=3x675+1, so 3^20263^1±od13. Hence the remainder is 3.

Arithmetic

Numericals

Medium

applied

The least non-negative remainder when $3^{2026}$ is divided by 13 is:

✅ Correct Option: 4

$3^3=27\equiv1\pmod{13}$ , so the powers of $3$ repeat with period $3$ .

$2026=3\times675+1$ , so $3^{2026}\equiv3^{1}\pmod{13}$ .

Hence the remainder is $3$ .

2025: 15 May Shift 1

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