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Squarely Divisible? (Posted on 2009-12-31) Difficulty: 1 of 5
Can there exist three integers p, q and r with 2 ≤ p < q < r, that satisfy each of the following conditions?

(i) p2 -1 is divisible by each of q and r, and:

(ii) r2 -1 is divisible by each of p and q.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Some Thoughts Extra credit Comment 2 of 2 |
By the way, note that my proof (see first posting) is stronger than the problem requested.

I have proven that there do not exist three integers p, q and r
with 2 ≤ p and p < q  and p < r, that satisfy each of the following conditions:

(i) p2 -1 is divisible by each of q and r, and:

(ii) r2 -1 is divisible by q. 

  Posted by Steve Herman on 2010-01-02 22:05:29
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