How many integers in [-10,10] are co-prime with 7?
I find that prime belongs to N, so my answer is 9(1,2,3,4,5,6,8,9,10).
can you give me advice?
Asked
Active
Viewed 208 times
0
-
As $7$ is prime, just remove from the given interval all multiples of $7$ (including negative ones). – Bernard Sep 20 '19 at 22:53
-
definition coprime: (also written co-prime) if the only positive integer (factor) that divides both of them is 1. so I think negative ones are not in it. – Jimmy Sep 20 '19 at 22:57
-
Why? $1$ divides negative numbers as well. – Bernard Sep 20 '19 at 23:01
-
According to the definition, coprime belongs to positive integers. – Jimmy Sep 21 '19 at 07:12
-
I'm sorry, but only prime numbers are defined as belonging to natural numbers. That is done to ensure uniqueness in the prime factors decomposition. There is no uniqueness involved in defining coprime numbers. Their definition can be extended to coprime ideals in rings. – Bernard Sep 21 '19 at 09:21
-
Wow, you are right, and I got it. Thanks! – Jimmy Sep 22 '19 at 11:22