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2007•Journal of Guangxi Teachers Education UniversityRequires access

On Makowski's Conjecture Concerning the Euler Totient Function

LE Mao-hua

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Abstract

For any positive integer n,let φ(n) denote the Euler's function of n.In this paper we prove that if φ(n+3)=φ(n)+2,then n∈2pr,2pr-3,where p is an odd prime with p≡3(mod 4),r is a positive integer.

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What this paper is about

For any positive integer n,let φ(n) denote the Euler's function of n.In this paper we prove that if φ(n+3)=φ(n)+2,then n∈2pr,2pr-3,where p is an odd prime with p≡3(mod 4),r is a positive integer.

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Available abstract

For any positive integer n,let φ(n) denote the Euler's function of n.In this paper we prove that if φ(n+3)=φ(n)+2,then n∈2pr,2pr-3,where p is an odd prime with p≡3(mod 4),r is a positive integer.

Key concepts: Euler's totient function, Mathematics, Integer (computer science), Prime (order theory), Euler's formula, Conjecture, Combinatorics, Function (biology)

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