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## Homework Statement

Solve in N^2 the following system of equations:

1- gcd(x,y)=7 and Lcm(x,y)=91

2- x+y=24 and Lcm =40

## The Attempt at a Solution

Let d=gcd(x,y)

I said there exists an α and β so that x=dα and y=dβ and gcd(α,β)=1

And after doing some work i reached that α divides αβ=13 so that gives only two solutions that satisfy gcd(α,β)=1 and they are α=1 and β=13 and vise versa. So I got S={(7,91);(91,7)}. Can someone help me with the second one. Thank you.

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