Question 4 : Let n be an integer number. Prove that the equation $\displaystyle x^{2}+y^{2}=n+z^{2}$ has infinitely many integer solutions.

Question 6 : Show that there are infinitely many systems of positive integers (x,y,z,t) which have no common divisor greater that 1 and such that<br>$\displaystyle x^{3}+y^{3}+z^{2}=t^{4}.$<br>

Question 9 : Sum of two integers is $+62$. If one of the integer is $-48$, then the other is

Question 12 : Consider equation $I : x + y + z = 46$ where $x, y$, and $z$ are positive integers, and equation II: $x + y + z + w = 46$, where $x, y, z$ and $w$ are positive integers. Then