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?

(In reply to Hint by K Sengupta)

In your hint regarding the second expression you raise (x+y) to the power of 7, but the exponetiation to (x+y) is absent in the problem text.

Posted by Dej Mar on 2007-04-19 02:21:34