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# number theory

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A no. when divided by 899 gives a remainder 63. The remainder when this no. is divided by 29 is what?

Jun 24, 2020

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A no. when divided by 899 gives a remainder 63.
The remainder when this no. is divided by 29 is what?

$$\begin{array}{|rcll|} \hline x \equiv 63 \pmod{899} &\text{or}& x = 63+899n, n \in \mathbb{Z} \\\\ x \pmod{29} &\equiv& 63+899n \pmod{29} \quad | \quad 63 \pmod{29} = 5,\ 899n\pmod{29}= 0 \\ &\equiv& 5+0 \pmod{29} \\ &\equiv& 5 \pmod{29} \\ \hline \end{array}$$

The remainder when this no. is divided by 29 is $$\mathbf{5}$$

Jun 24, 2020