Prove that Euler\'s function (n) approaches infinity as n approaches infinity So

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Prove that Euler's function (n) approaches infinity as n approaches infinity

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Dear Student Thank you for using Chegg !! Let N be a positive integer and let p be the leaast prime number greater than N+1 Let n be an integer such that (n) = N If q>p is a prime divisor of x, then x=(q^k).m for some k>1 and m with q not dividing m (n) = (q^k). (m) > q-1 > p-1 >N,    a contradiction Thus no prime divisor of n is greater than N+1 . In particular, the distinct prime divisors of n belong to a finite set; say these primes are . p1,p2,p3…………………………..pm Now we can write n= p1a1 . P2a2 ……………………………………………….pmam for some 0 (piai-1)(pi-1) >N for sufficiently large ai Thus for each pi, there exists only finite many permissible choices for the exponents ai, So the set of all n, with (n) = N . Thus as n approaches infinity, so does (n) Hence prooved

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