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Old 2017-02-25, 23:00   #2
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

13168 Posts
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Hi Mersenneforum,

In order to tackle this first number theory problem,
(okay it is problem 84)
I will try a similar problem.
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.
My education has a gap here.

I use my Maple computer tool to conclude that x is congruent to 2*x+1 mod 7.
Here is my Maple code –

a:=-(5*x+6) mod 7

And, again, Maple returns a= 2*x+1 mod 7.
Maybe someone can help me fill in the gaps.
Regards,
Matt
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