Đặt $a=2x-1,b=2x+y,c=1-3x$
$\to a+b+c=x+y$
Khi đó ta có : $P = a^5+b^5+c^5$ và $P = a+b+c$
Xét hiệu $P-S=a^5+b^5+c^5-a-b-c$
$ =a.(a^4-1)+b.(b^4-1)+c.(c^4-1)$
$ = (a-1).a.(a+1).(a^2+1) + (b-1).b.(b+1).(b^2+1)+(c-1).c.(c+1).(c^2+1)$
$ = (a-1).a.(a+1).(a^2-4+5) + (b-1).b.(b+1).(b^2-4+5)+(c-1).c.(c+1).(c^2-4+5)$
$ = (a-2).(a-1).a.(a+1).(a+2)+5.a.(a-1).(a+1) + (b-2).(b-1).b.(b+1).(b+2)+5.b.(b-1).(b+1)+(c-2).(c-1).c.(c+1)(c+2)+5.(c-1).c.(c+1) \vdots 30$
Do đó : $P - S \vdots 30$ mà $P \vdots 30$
$\to S \vdots 30$ $\to đpcm$
