(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a_1, a_2, b_1, b_2 are all positive integers greater than one.

Given that (a_2-1)/(a_1*a_2-1)=(b_2-1)/(b_1*b_2)

Show that GCD(a_2-1,a_1*a_2-1,b_2-1,b_1*b_2)=1

2. Relevant equations

(a_2-1)/(a_1*a_2-1)=(b_2-1)/(b_1*b_2)

3. The attempt at a solution

If I let the GCD=d, then d|a_2-1 and d|a_1*a_2-1, so this implies that d|a_1*a_2-a_2+1-1

-> d|a_1*a_2-a_2

-> d|a_2(a_1-1)

-> d|a_1-1 since d does not divide a_2

Also, since d|b_1*b_2, and d does not divide b_2 (due to the fact that d|b_2-1), d|b_1.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Question on finding the GCD of 4 numbers

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