(New page: Show that <math> 5*n + 3 </math> and <math> 7*n + 4 </math> are relatively prime. <math> 7*n + 4 = 5*n + 3 + 2*n + 1 5*n + 3 = 2*(2*n + 1) + n + 1 2*n + 1 = 1*(n + 1) + n n + 1 = 1*n + 1...) |
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Show that <math> 5*n + 3 </math> and <math> 7*n + 4 </math> are relatively prime. | Show that <math> 5*n + 3 </math> and <math> 7*n + 4 </math> are relatively prime. | ||
<math> | <math> | ||
| − | 7*n + 4 = 5*n + 3 + 2*n + 1 | + | 7*n + 4 = 5*n + 3 + 2*n + 1<br> |
5*n + 3 = 2*(2*n + 1) + n + 1 | 5*n + 3 = 2*(2*n + 1) + n + 1 | ||
2*n + 1 = 1*(n + 1) + n | 2*n + 1 = 1*(n + 1) + n | ||
Revision as of 20:13, 6 September 2008
Show that $ 5*n + 3 $ and $ 7*n + 4 $ are relatively prime. $ 7*n + 4 = 5*n + 3 + 2*n + 1<br> 5*n + 3 = 2*(2*n + 1) + n + 1 2*n + 1 = 1*(n + 1) + n n + 1 = 1*n + 1 $
After constant long division we get to the base equation where there is still a remainder of 1. Therefore $ 5*n + 3 $ and $ 7*n + 4 $ are relatively prime.
