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April 12th, 2014, 12:10 PM   #1
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if we divide n by 7 rest =3

if we divide 5n+4 by 7 what the rest
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April 12th, 2014, 01:28 PM   #2
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5x3 + 4 = 19, mod 7 = 5.
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April 12th, 2014, 05:37 PM   #3
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Hello, mared!

Quote:
If we divide $\displaystyle n$ by 7, the remainder is 3.
What is the remainder if we divide $\displaystyle 5n+4$ by 7 ?

We are told that: $\displaystyle \;n \:=\:7a+3$ for some integer $\displaystyle a.$

Then $\displaystyle \:5n+4 \;=\;5(7a+3)+4 \;=\;35a + 15 + 4 \;=\;35a + 19$

Hence: $\displaystyle \;\frac{5n+4}{7} \;=\; \frac{35a+19}{7} \;=\;5a + 2 + \frac{5}{7}$

Therefore, the remainder is $\displaystyle 5.$

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