Find the inverse function f(x)=x+[x].

Find six distinct positive integers A, B, C, D, E, F, G satisfying:

A^{3} + B^{3} = C^{3} + D^{3} = E^{3} + F^{3} = 19G^{3}.

Please submit primitive solutions only, that is, A, B, C, D, E, F, G should not have a common factor.

Out of 26 ABCâ€™s letters I have erased 15, leaving only those:

**a,e,i,j,k,o,q,u,v,x,y.**

What were my criteria?

Consider the sum 1^99 + 2^99 + 3^99 + ... + 99^99.

Finding the last digit of this sum was the task of an old problem

Last Digit. With a clever setup finding the last two digits was just as easy.

So I present a higher challenge: find the last four digits. No computer programs!