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Making integer an expression (Posted on 2009-03-20) Difficulty: 2 of 5
Find all positive integers n which make the expression below an integer:

(25/2 + (625/4 - n)½ )½ + (25/2 - (625/4 - n)½ )½

See The Solution Submitted by pcbouhid    
Rating: 3.0000 (1 votes)

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Hints/Tips Just the math | Comment 7 of 13 |
By the way, kudos to pcbouhid for coming up with an expression that simplifies so nicely when squared.  Lots of terms cancel out.  I didn't include the math in my solution,  but the square of the expression above =

(25/2 + (625/4 - n)½ ) + (25/2 - (625/4 - n)½ ) +
2(25/2 + (625/4 - n)½ )½ (25/2 - (625/4 - n)½ )½   =

25 +
2(25/2 * 25/2 - (625/4 - n) )½  =

25 + 2n½
  Posted by Steve Herman on 2009-03-21 18:04:38
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