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Phi of consecutive numbers are power of 2

Source: India Postal Set 1 P1 2016

January 18, 2017

number theory

Problem Statement

Let

n

be an odd positive integer such that

\varphi (n)

and

\varphi (n+1)

are both powers of

2

(here

\varphi(n)

denotes Euler’s totient function). Prove that

n+1

is a power of

2

or

n = 5

.

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