Prove that for any positive integer
there exist an infinite number of pairs of integers
such that
(i)
and
are relatively prime;
(ii)
divides
;
(iii)
divides
(iv)
(optional condition)
%V0
Prove that for any positive integer $m$ there exist an infinite number of pairs of integers $(x, y)$ such that
(i) $x$ and $y$ are relatively prime;
(ii) $y$ divides $x^2 + m$;
(iii) $x$ divides $y^2 + m.$
(iv) $x + y \leq m + 1-$ (optional condition)
Školjka