Determine at least three pairs of positive integers (x,y) with x< y such that xy(x+y) is not divisible by 7, but (x+y)⁷ - x⁷ - y⁷ is divisible by 7⁷

Does the given problem generate an infinite number of pairs as solutions?

Can you do this in a short time using pen and paper, and eventually a hand calculator, but no computer programs?

For xy(x+y) not divisible by 7 and (x+y)⁷ - x⁷ - x⁷ divisible by 7⁷, a list of some of the positive integer pairs (x, y),
with x < y, are...

(15, 58), (16, 39), (17, 20),
and (n, 18n) {(1, 18), (2, 36), (3, 54), ...} where n >= 1 confirmed to n=7, thus appearing to generate an infinite number of pairs as solutions   

Edited on April 19, 2007, 2:56 am

Posted by Dej Mar on 2007-04-19 02:52:21