Conceptual

Number Theory Level 2

What is the remainder when -1 is divided by 3?

Clarification : By convention, the remainder must be a non-negative number.

3 3 − 1 -1 − 2 -2 Not defined − 3 -3 2 2 1 1 0 0

Akhil Bansal by Akhil Bansal , 22, India

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2 solutions

Nihar Mahajan
Dec 21, 2015

− 1 ≡ − 1 + 3 ≡ 2 ( m o d 3 ) \Large -1 \equiv -1+3 \equiv \boxed{2} \pmod{3}

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Pulkit Gupta
Dec 21, 2015

One thing to learn and remember from this is that a remainder is ALWAYS a positive number.

Now, − 1 = 3 ∗ ( − 1 ) + 2 \large -1 = 3 * (-1) + 2 . Hence, 2 is the answer.

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