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Divisible by 3. (Posted on 2012-12-02) Difficulty: 2 of 5
Let p and q be two different prime numbers greater than 3.Prove that if their difference is 2^n, then for any two integers n and m,the number S=p^(3m+1)+q^(2m+1) is divisible by 3.

Let p and q be two different prime numbers greater than 3.
Prove that if their difference is 2n, then for any two integers n and m,
the number S = p(3m+1) + q(2m+1) is divisible by 3.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (2 votes)

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Some Thoughts Some thoughts | Comment 1 of 5

Let n=1; let m=1.

Let p=5, then q=7. 5^(3m+1) =625, 7^(2m+1)=343.

343+625=968, which is 2^3*11^2, not divisible by 3.

Let n=1; let m=1.

Let p=11, then q=13. 11^(3m+1) =14641, 13^(2m+1)=2197.

14641+2197=16838, which is 2*8419, not divisible by 3.

 

Edited on December 2, 2012, 11:31 am
  Posted by broll on 2012-12-02 11:23:10

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