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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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Some Thoughts another humble step forward | Comment 2 of 4 |

For 3 consecutive terms of AP: a-d  a  & a+d

sum of cubes equals 3*a^3+6a*d^2 and is divisible by 3

 

so far so good


  Posted by Ady TZIDON on 2008-03-06 12:42:29
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