perplexus.info :: Just Math : Divisible by 3.

Divisible by 3. (Posted on 2012-12-02)

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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Confusing problem

| Comment 2 of 5 |

This is a confusing problem for the following reasons.

1. It repeats twice in the problem. The first time, it uses ^ for powers. The second time, it uses superscripts.

2. It says, "For any two integers n and m, the number p^(3m+1)+q^(2m+1) is divisible by 3." However, the number n does not appear in p^(3m+1)+q^(2m+1).

3. It is wrong. For example, take p=5, q=13, m=1. q-p=8=2^3, but p^(3m+1)+q^(2m+1)=5^4+13^3=625+2197=2822 is not divisible by 3.

Posted by Math Man on 2012-12-02 13:46:37

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