BMAD Posted March 20, 2015 Report Share Posted March 20, 2015 Let w be the greatest common divisor of m and n. Show that 3w − 1 is the greatest common divisor of 3m − 1 and 3n−1. Quote Link to comment Share on other sites More sharing options...
0 Rainman Posted March 21, 2015 Report Share Posted March 21, 2015 Assume WLOG that m≥n. Wouldn't it just be GCD(3m-1, 3n-1) = 3n-1? Clearly 3n-1 divides itself and is the greatest possible divisor of itself, and 3m-1 = 3n-1*3m-n, so 3n-1 divides 3m-1 as well. Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted March 21, 2015 Author Report Share Posted March 21, 2015 where does 3w − 1 fit? Quote Link to comment Share on other sites More sharing options...
0 k-man Posted March 23, 2015 Report Share Posted March 23, 2015 I think Rainman is questioning the correctness of the OP as it's asking to show something that's not true. Let's take m=8 and n=10. Then w=GCD(8,10)=2. But GCD(37,39)=37 and not 3. Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted March 23, 2015 Author Report Share Posted March 23, 2015 Let w be the greatest common divisor of m and n. Show that 3w − 1 is the greatest common divisor of 3m − 1 and 3n−1. AHH.. I see the error in my op. What I mean is: Show that 3w - 1 is the GCD of 3m - 1 and 3n - 1; i mistakenly raised the ' - 1 ' Quote Link to comment Share on other sites More sharing options...
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BMAD
Let w be the greatest common divisor of m and n. Show that 3w − 1 is the greatest common divisor of 3m − 1 and 3n−1.
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