Find a: Solve Discrete Math Problem with a & x Intergers

[boiseneon]

ok the problem is

Given that a and x are intergers, a>1, a|(11x+3), a|(55x+52), find a.

I am not sure how to even start this one to find a...any help please

 

[Muzza]

There are integers p, q such that

11x + 3 = pa,
55x + 52 = qa.

Try eliminating x...

 

[boiseneon]

ok how do I eliminate x??

 

[C0nfused]

I am not at all familiar with number theory but I think got the answer:
First of all we have a>1>0 and x>0

11x+3=pa<=>55x+15=5pa (1)
55x+52=qa (2)

(2)-(1)=>37=(q-5p)a
q,p are natural numbers
So a|37 and 37 is a prime=> ...