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2017-02-26, 10:09   #4
Nick

Dec 2012
The Netherlands

13·127 Posts

Quote:
 Originally Posted by MattcAnderson 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!