Show that Z (integers) is generated by 5 and 7.

I can sit and play with those two numbers to get all Z, but can't come up with a formula. Can someone show how to do this?

Thanks

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- Sep 19th 2012, 11:45 PMjzelltAbstract Algebra
Show that Z (integers) is generated by 5 and 7.

I can sit and play with those two numbers to get all Z, but can't come up with a formula. Can someone show how to do this?

Thanks - Sep 20th 2012, 01:31 AMFernandoRevillaRe: Abstract Algebra
- Sep 20th 2012, 01:34 AMjzelltRe: Abstract Algebra
Thanks! That's brilliant!

- Sep 20th 2012, 01:39 AMFernandoRevillaRe: Abstract Algebra
- Sep 20th 2012, 05:27 AMDevenoRe: Abstract Algebra
the subgroup of Z generated by the integers k and m is: <gcd(k,m)>. if two numbers are co-prime, they generate all of Z, since 1 generates Z (Z is cyclic).