Each of exercises 51-53 refers to the Euler phi function, denoted , which is defined as follows: For each integer is the number of positive integers less than or equal to n that have no common factors with n except . For example, because there are four positive integers less than or equal to 10 that have no common factor with 10 except -namely, 1,3,7, and9.
Prove that there are infinitely many integers n for which is a perfect square.
There are infinitely many integers for which is a perfect square.
When is a prime number and is an integer with , then
The objective is to prove that there are infinitely many integers for which is perfect square.
If is prime then,
Put (Since is a prime number) in equation , to obtain.
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