<span>Решение на фото, которое прикреплено</span>
<span>18 ПРЕДСТАВИТЬ КАК (12 + 6),возводим в квадрат, </span>
<span>=144+144+36=2*144+36 - опять в квадрат</span>
<span>4*12^4+144*12^2+6^4=5*12^4+6^4 - это вычитаем из 12^5 </span>
<span> 12*12^4 - 5*12^4 - 6^4 = 7*12^4 - 6^4 = 6^4(7*2^4 - 1)= </span>
<span>=6^4(7*16 - 1) = 6^4( 111 ), а 111делится на 37 без остатка, вот и решение</span>
![x+y=\pi => x=\pi-y](https://tex.z-dn.net/?f=x%2By%3D%5Cpi+%3D%3E+x%3D%5Cpi-y)
![sin(\pi-y)+siny=1](https://tex.z-dn.net/?f=sin%28%5Cpi-y%29%2Bsiny%3D1)
![siny+siny=1](https://tex.z-dn.net/?f=siny%2Bsiny%3D1)
![y=(-1)^k\frac{\pi}{6}+\pi k,k \in Z](https://tex.z-dn.net/?f=y%3D%28-1%29%5Ek%5Cfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi+k%2Ck+%5Cin+Z)
Значит
![x=(-1)^{k-1}\frac{\pi}{6}-\pi (k-1),k \in Z](https://tex.z-dn.net/?f=x%3D%28-1%29%5E%7Bk-1%7D%5Cfrac%7B%5Cpi%7D%7B6%7D-%5Cpi+%28k-1%29%2Ck+%5Cin+Z)
Сложим оба равенства для проверки:
![x+y=(-1)^k\frac{\pi}{6}+\pi k+(-1)^{k-1}\frac{\pi}{6}-\pi (k-1)=\frac{\pi}{6}((-1)^k+(-1)^{k-1})+\pi k-\pi k+\pi=\frac{\pi}{6}*0+\pi=\pi](https://tex.z-dn.net/?f=x%2By%3D%28-1%29%5Ek%5Cfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi+k%2B%28-1%29%5E%7Bk-1%7D%5Cfrac%7B%5Cpi%7D%7B6%7D-%5Cpi+%28k-1%29%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%28%28-1%29%5Ek%2B%28-1%29%5E%7Bk-1%7D%29%2B%5Cpi+k-%5Cpi+k%2B%5Cpi%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%2A0%2B%5Cpi%3D%5Cpi)