Question 33
Find all pairs of positive integers $(a, b)$ satisfying the following conditions:
(i) $a$ divides $b^4 + 1$,
(ii) $b$ divides $a^4 + 1$,
(iii) $\lfloor\sqrt{a}\rfloor = \lfloor\sqrt{b}\rfloor$.
(i) $a$ divides $b^4 + 1$,
(ii) $b$ divides $a^4 + 1$,
(iii) $\lfloor\sqrt{a}\rfloor = \lfloor\sqrt{b}\rfloor$.