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Old 2017-02-26, 10:09   #4
Nick
 
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Dec 2012
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Quote:
Originally Posted by MattcAnderson View Post
Find all x such that
5*x+6 is congruent to 0 mod 7 expression 1

From the reading, I notice that the greatest common divisor of 5 and 6 is 1. So the techniques presented here should apply.

We make an augmented T table

X 5*X 5*X mod 7
______________________
0 0 0
1 5 5
2 10 3
3 15 1
4 20 6
5 25 4
6 30 2

From expression 1, conclude that 5*x is congruent to 1 mod 7.
Yes, and only one row in your table has 5x mod 7 = 1...

An alternative approach is to multiply by 3 (because 3x5 mod 7=1):
if \(5x+6\equiv 0\pmod{7}\) then \(3(5x+6)\equiv 0\pmod{7}\)
and so \(x+4\equiv 0\pmod{7}\).

I hope this helps!
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