Question

СРОЧНО (40 баллов)
Решите:
$( {43}^{2} - 1)\times ( {43}^{2} - 2)\times...\times ( {43}^{2} - 5000)$
*Примечание: всего 5000 множителей​

Answer 1

$( {43}^{2} - 1)\times ( {43}^{2} - 2)\times...\times ( {43}^{2} - 5000)=\\\\ ( 1849- 1) \times ( 1849- 2) \times... \times (1849 - 5000)=\\\\1848 \times  1847 \times... \times (-3151)=\\\\ ( {43}^{2} - 1)\times ( {43}^{2} - 2)\times...\times ( {43}^{2} - 5000)=\\\\ ( 1849- 1) \times ( 1849- 2) \times... \times (1849 - 5000)=\\\\1848 \times  1847 \times... \times0 \times ... \times (-3151)=0$