If p, q are integers so that q>p>1, show that 1/p+ 1/(p+1)+ 1/(p+2)+ ... +1/q cannot be an integer.

(In reply to Solution by David Shin)

Very perceptive! Among the positive integers, 2 appears to uniquely enjoy the property that its largest power dividing given consecutive positive numbers divides only one of them.

I read somewhere online that the reciprocals of any arithmetic progression can't add to an integer.

Posted by Richard on 2004-10-07 14:49:26