Sorry, Im not really sure where this should get posted.
Prove the following:
if gcd (a,n)=1 then the integers
c,c+a,c+2a,c+3a,...,c+(n-1)a
for a complete set of residues modulo n for any c.
so far I know that any integer will be equal to 0,1,2,...(n-1) mod n
my prof said to show that i does not equal j and therefore c+ia does not equal c+ja.
well i think its kinda obvious that the cofficients of a are never equal but is there a more mathematical way of proving this.
and another: The product of any set of n consecutive integers is divisible by n.
my thoughts are that one of those integers will always be equal to 0 mod(n) and therefore 0 times anything will be 0 so the whole product will be equal to 0 mod(n) which means it is divisible by n.
Is this the right track?
Thanks!
Prove the following:
if gcd (a,n)=1 then the integers
c,c+a,c+2a,c+3a,...,c+(n-1)a
for a complete set of residues modulo n for any c.
so far I know that any integer will be equal to 0,1,2,...(n-1) mod n
my prof said to show that i does not equal j and therefore c+ia does not equal c+ja.
well i think its kinda obvious that the cofficients of a are never equal but is there a more mathematical way of proving this.
and another: The product of any set of n consecutive integers is divisible by n.
my thoughts are that one of those integers will always be equal to 0 mod(n) and therefore 0 times anything will be 0 so the whole product will be equal to 0 mod(n) which means it is divisible by n.
Is this the right track?
Thanks!