Identity in number theory

Feb 2010
114
0
Is the following statement correct?

If gcd\(\displaystyle (a, m)=m\), then \(\displaystyle a^m\equiv 0\) (mod \(\displaystyle m\))
 
Jan 2009
463
138
Using the equivalent form of the modulo statement, we have:
\(\displaystyle a^m = km\), which implies
\(\displaystyle k = a^{m-1} * \frac{a}{m}\)

With m > 0 and gcd(a,m) = m, k is an integer and we can conclude the statement is correct.
 
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