If a and b are both odd, write a = 2A-1 and b = 2B-1, so that aČ - bČ = (a-b)(a+b) = 4(A-B)(A+B-1) is divisible by 4. But aČ + bČ=4(AČ-A+BČ-B)+2 is not divisible 4. Hence, the fraction is not an integer.
Next look at the case with b=2: by inspection, a=3 does not yield an integer. But with a>3 we have
aČ - 4 < aČ + 4 < 2(aČ - 4)
hence no integer here either.
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Posted by FrankM
on 2008-01-05 22:47:14 |
Alternative solution
