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Floor and Square Division Settlement (Posted on 2016-01-01) Difficulty: 3 of 5
Find all possible positive integers P, which are not perfect squares, such that (floor(√P))3 divides P2

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

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re(2): answer | Comment 3 of 4 |
(In reply to re: answer by broll)

My sentiment exactly.  It's not hard to find P={2,3,8,24}
I am able to show that P=n²-1 for only n=2,3,5
but its pretty messy
and that P=n²-2 for only n=2
is even messier

but to show these are the only possibilities I haven't done.  In fact there may be more.

  Posted by Jer on 2016-01-02 12:23:49

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