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## Main Question or Discussion Point

Hi everyone, this is not a homework question just a math puzzle I came across.

Let [itex]a[/itex] and [itex]b[/itex] be any two natural numbers. And let [itex] (m,n) [/itex] denote the GCD of [itex]m[/itex] and [itex]n[/itex] as usual. Prove [tex] (2^{a}-1,2^{b}-1) = 2^{(a,b)}-1 [/tex]

I'm thinking of double induction on [itex]a[/itex] and [itex]b[/itex] but I'm having trouble with the inductive steps.

Does any know how to do this? If so, any hints?

Let [itex]a[/itex] and [itex]b[/itex] be any two natural numbers. And let [itex] (m,n) [/itex] denote the GCD of [itex]m[/itex] and [itex]n[/itex] as usual. Prove [tex] (2^{a}-1,2^{b}-1) = 2^{(a,b)}-1 [/tex]

I'm thinking of double induction on [itex]a[/itex] and [itex]b[/itex] but I'm having trouble with the inductive steps.

Does any know how to do this? If so, any hints?