Quote:
Originally Posted by MattcAnderson
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

but this equation isn't quadratic.
edit:
the solution like this for 84 is similar to this: