Numerical answer
What is the remainder when 3²⁵⁶ is divided by 17?
Show answer and solution
Answer: 1
17 is prime, so by Fermat's little theorem 3¹⁶ ≡ 1 (mod 17).
256 = 16 × 16, so 3²⁵⁶ = (3¹⁶)¹⁶ ≡ 1¹⁶ = 1 (mod 17).
Remainder = 1.
Tip: When the exponent is an exact multiple of (p − 1), the remainder is 1 immediately — check for this special case before doing any further reduction.
256 = 16 × 16, so 3²⁵⁶ = (3¹⁶)¹⁶ ≡ 1¹⁶ = 1 (mod 17).
Remainder = 1.
Tip: When the exponent is an exact multiple of (p − 1), the remainder is 1 immediately — check for this special case before doing any further reduction.
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