Euler’s totient function???

Plz…can anyone explain me this and whats the use for it …I have read the topcoder but could not understand it…

number of positive integers less than or equal to n that are relatively prime to n(i.e gcd==1).
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The totient function, denoted by phi(n) is defined as the number of positive integers (<=n) which are relatively prime i.e. they do not have any factor in common with n, where 1 is being counted as relatively prime with every number. Any such number(<=n) and co-prime with n is called a totative and hence the function is called totient function.
eg: phi(24) = 8 where the possible such numbers are 1,5,7,11,13,17,19,23.

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