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Prime as sum of Cubes of terms of AP? (Posted on 2008-03-02) Difficulty: 2 of 5
Let Si be the ith term of an Arithmetic Progression whose 1st term is a and common difference d. Show that for any 2 positive integers m,n(>m), Σ(i:m to n)(Si)3 can't be a prime number.

Note: a,d are positive integers.

See The Solution Submitted by Praneeth    
Rating: 3.3333 (3 votes)

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A humble start | Comment 1 of 4

 

It is surely true for the sum  of the two 1st members: a  and a+d,

  denote a+d  by b:

 

 a^3+b^3=(a+b)*(a^2-ab+b^2)     ==>  is not prime/

  From here  I don't know how to follow

Ady

 


  Posted by Ady TZIDON on 2008-03-03 16:31:20
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