perplexus.info :: Just Math : Not an Integer!

Not an Integer! (Posted on 2007-10-07)

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 solution	FrankM	2008-01-05 22:47:14
A possible solution...	lpriya	2007-10-16 07:50:59
Square root from an positive integer can't be a fraction!	Chesca Ciprian	2007-10-09 10:40:08
Parts of a whole	Gamer	2007-10-08 20:30:45
No way	Steve Herman	2007-10-07 22:44:25

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