Question 21
(USS 1) Let $N$ be the number of integral solutions of the equation
$$x^2-y^2=z^3-t^3$$
satisfying the condition $0\le x,y,z,t\le10^6$, and let $M$ be the number of integral solutions of the equation
$$x^2-y^2=z^3-t^3+1$$
satisfying the condition $0\le x,y,z,t\le10^6$. Prove that $N\gt M$.
$$x^2-y^2=z^3-t^3$$
satisfying the condition $0\le x,y,z,t\le10^6$, and let $M$ be the number of integral solutions of the equation
$$x^2-y^2=z^3-t^3+1$$
satisfying the condition $0\le x,y,z,t\le10^6$. Prove that $N\gt M$.