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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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re official solution -- IS NOT PERFECT Comment 4 of 4 |

 a.  the oficial solution asumes even number of members

b. the mean is not nessarily an integer

c The sum of cubes is divisible by the sum of MEMBERS

If  no one provides a formal proof  within  a week -I  will do it, despite my laziness

Hint: there are 2 seperate proofs: for m-n being odd or even

  Posted by Ady TZIDON on 2008-03-08 19:45:10
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