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

AI Thread Summary
The problem involves finding integer values for a and x, given the conditions a > 1 and that a divides both 11x + 3 and 55x + 52. The discussion highlights the approach of expressing the equations in terms of integers p and q, leading to the equations 11x + 3 = pa and 55x + 52 = qa. By manipulating these equations, the user eliminates x and derives the relationship 37 = (q - 5p)a. Since 37 is a prime number, the only possible values for a are its divisors, which leads to the conclusion that a must be 37.
boiseneon
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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 :cry:
 
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There are integers p, q such that

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

Try eliminating x...
 
ok how do I eliminate x??
 
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=> ...
 

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