Thread: Abstract 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

Originally Posted by jzellt

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

For all we have

Thanks! That's brilliant!

Originally Posted by jzellt

Thanks! That's brilliant!

Not very brilliant . It is a particular case of the Bezout equallity.

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).