# Prove that for any given positive integer N there exist at most finitely many integersdenotes the Euler totient function. Conclude inn with(n)N, whereparticular that (n) tends to infinity as n tends to infinity.

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Asked Jul 27, 2019
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Question attached.  I have found solutions to this probem on the internet, but I don't understand the explanations.  Can you provide a "layman's terms" explanation?  Thanks.

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## Expert Answer

Step 1

Let N be a given positive integer and let p be the least prime number greater than N + 1.

Let n be an integer such that

Step 2

If q > p is a prime divisor of n, then n = (qk) m for some k > 1and m with q not diving m.

Step 3

It is contraction to our assumption.

Thus, there is no prime divisor of n is greater than N + 1.

In p...

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