If m is a positive integer, can m(m+1) be the 7th power of an integer?

m and m+1 can have no common factors, so m and m+1 would individually have to be 7th powers. But two consecutive numbers can't both be 7th powers, except for the trivial case 0^7 and 1^7, and zero is not a positive integer.

Posted by Charlie on 2013-07-08 13:53:23