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Find the smallest positive integer $N$ that satisfies the system of congruences
\begin{align*}
N &\equiv 2 \pmod{3}, \\
N &\equiv 2 \pmod{7}, \\
N &\equiv 2 \pmod{10}.
\end{align*}

Sagot :

Sqdancefanidn

Answer:

  2

Step-by-step explanation:

You want the smallest positive integer N such that N ≡ 2 modulo 3, 7 or 10.

Remainder

The smallest integer that will have a remainder of 2 when divided by 3, 7, or 10 will be 2.

  N = 2

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Additional comment

Additional solutions will be 2+210k, where k is a positive integer.

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