Find all possible couples of distinct integers (x,y) satisfying the equation: **
x^4 + y = x^3 + y^2**

When you were born, both of your rich grandparents made a deal with your parents, to do with what money they'll give you for birthdays. Grandad's deal was :

*I'll give you £1 for your first birthday. Then, the amounts that I give you each year will double every time*

and Grandma said :

*I will start by giving you £1 for your first birthday. Then, the amount I give you will be the combined total of all the last birthday presents that I have ever given you up to that point. Plus, every birthday you have that's a multiple of five, I'll give you an extra five pounds.*

a)What amount of money do they each pay you for your 15th birthday

and

Who would have given you the most after 27 years?