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Not an Integer! (Posted on 2007-10-07) Difficulty: 3 of 5
If a and b are distinct positive integers, then show that (a2+b2)/(a2-b2) can not be an integer.

  Submitted by Praneeth    
Rating: 4.0000 (4 votes)
Solution: (Hide)
The given expression can be reduced to (p2+q2)/(p2-q2) where p,q are relatively primes to each other.
Now, (p2-q2) should divide 2*p2 and 2*q2 at the same time.
As p2 and q2 are relatively prime to each other, (p2-q2) should divide 2 which is impossible.
Hence Proved. Other Solution is provided by Chesca Ciprian

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Alternative solutionFrankM2008-01-05 22:47:14
A possible solution...lpriya2007-10-16 07:50:59
Square root from an positive integer can't be a fraction!Chesca Ciprian2007-10-09 10:40:08
Parts of a wholeGamer2007-10-08 20:30:45
SolutionNo waySteve Herman2007-10-07 22:44:25
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