Question Number 56912 by Kunal12588 last updated on 26/Mar/19
$$\mathrm{If}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\left(\mathrm{1}+{ab}\right)\:\mathrm{divides}\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{integer} \\ $$$$\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{1}+{ab}}\:\mathrm{must}\:\mathrm{be}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$
Commented by kaivan.ahmadi last updated on 26/Mar/19
$${I}\:{guess}\:{I}\:{and}\:{mrW}\:{have}\:{solved}\:{this} \\ $$$${question}\:{by}\:{two}\:{way} \\ $$
Commented by Kunal12588 last updated on 27/Mar/19
$${question}\:{number}\:{please} \\ $$
Commented by kaivan.ahmadi last updated on 27/Mar/19
$${No}.\mathrm{53618} \\ $$
Commented by kaivan.ahmadi last updated on 27/Mar/19
Answered by kaivan.ahmadi last updated on 27/Mar/19
