If n is a whole number with remainder 3 upon division by 4, what is the remainder when 2n is divided by 4?

Given data

• n ≡ 3 (mod 4)

Concept / Approach

• Multiply the congruence by 2 and reduce modulo 4.

Step-by-step calculation

2n ≡ 2 × 3 ≡ 6 (mod 4)6 ≡ 2 (mod 4)

Verification

Example check: n = 3 ⇒ 2n = 6 ⇒ 6 ÷ 4 leaves remainder 2.

Common pitfalls

• Assuming doubling preserves the same remainder; it does not necessarily under modular reduction.

Final Answer

2