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N 3

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May 25, 2007
modular arithmeticnumber theoryrelatively primeMore Sequences

Problem Statement

Let  n>6 \,n>6\, be an integer and  a1,a2,…,ak \,a_{1},a_{2},\ldots,a_{k}\, be all the natural numbers less than nn and relatively prime to nn. If a2−a1=a3−a2=⋯=ak−ak−1>0,a_{2}-a_{1}=a_{3}-a_{2}=\cdots =a_{k}-a_{k-1}>0, prove that  n \,n\, must be either a prime number or a power of  2\,2.
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