Context probably irrelevant but modular forms- to show that all rational numbers can be mapped to ##\infty##) that is there exists a ## \gamma = ( a b c d) ##, sorry thats a 2x2 matrix, ## \in SL_2(Z) ## with ## det (\gamma) = ad-bc=1 ## s.t ## \gamma . t = at+b/ct+d = \infty ##, where take ## t= r ## , r a rational number. )(adsbygoogle = window.adsbygoogle || []).push({});

So I'm at the stage where I am just stuck on showing that ## p ## and ## q ## co prime implies that ## b ## and ## d ## can be found s.t ## pd-bq=1 ## , b and d integer.

I'm not sure how to do this? I think the argument should be obvious?

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# I Show that you can find d and b s.t pd-bq=1 , p and q are coprime- GCF

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