perplexus.info :: Just Math : Squarely Divisible?

Squarely Divisible? (Posted on 2009-12-31)

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.

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

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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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