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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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Solution Simplifying matters (Spoiler) | Comment 2 of 13 |
Well, the square of the expression above is 25 +2n½

Set k = the square root of 25 +2n½

Then n = ((k*k - 25)/2)^2

This is positive and integral whenever k is an odd number > 5

k = 7 --> n = 12*12 = 144
k = 9 --> n = 28*28 = 784
k = 11 --> n = 48*48 = 2304

etc.

  Posted by Steve Herman on 2009-03-20 13:14:55
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