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

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

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solution | Comment 3 of 12 |
Consider the given expression to be a function.

The domain is {x|0<=x<=156.25}
so there aren't many values to check.
f(625/4)=f(156.25)=sqrt(50) = 7.071
and the function is increasing.  (Dont ask for a proof)
So we can only have f(x)=6 and f(x)=7

It turns out f(121/4)=6 and f(144)=7

so the only positive integer that yields and integer is 144.

  Posted by Jer on 2009-03-20 13:22:09
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