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- The number of summands $\phi(n)$ 1 answer
I am stuck with the following problem that says:
If $n$ is a positive integer such that the sum of all positive integers $a$ satisfying $1 \le a \le n$ and GCD $(a,n)=1$ is equal to $240n,$ then the number of summands ,namely,$\phi(n),$ is
MY TRY: Just for understanding, if I take $n=5,$then $a_i$'s such that gcd $(a_i,5)=1$ and $\sum a_i=240\times 5$. But, $a_i$'s can only be $1,2,3,4$ ,since $n=5$. Now, I do not know which way to go.
Can someone explain? Thanks in advance for your time.