W. 4

Part of 2009 Jozsef Wildt International Math Competition

Problems(1)

Problem on euler's totient fumction

Source: 2009 József Wildt International Mathematical Competition

\Phi

denote the Euler totient function. Prove that for infinitely many

k

\Phi (2^k+1) < 2^{k-1}

and that for infinitely many

m

\Phi (2^m+1) > 2^{m-1}

number theorytotient functionfunction