不定方程x(x+1)(x+2)(x+3)=33y(y+1)(y+2)(y+3)的整数解的研究
A Research of the Integer Solution of the Diophantine Equation x(x+1)(x+2)(x+3)=33y(y+1)(y+2)(y+3)

$主要运用Pell方程、递推序列、同余式及(非)平方剩余等一些初等的证明方法，对不定方程 $ x(x + 1)(x + 2)(x + 3) = 33y(y + 1)(y + 2)(y + 3) $ 的解进行了研究.证明了该不定方程仅有1组正整数解(x，y)=(9，3).同时给出了不定方程(x²+3x+1)²-33y²=-32的全部整数解.$
$In this paper, with such elementary methods as Pell equation, recurrence sequence, congruent form and quadratic (non-)residue, the author studies the diophantine equation $ x(x + 1)(x + 2)(x + 3) = 33y(y + 1)(y + 2)(y + 3) $ and shows that its only solution in positive integers is (x, y))=(9, 3). She also obtains all the integer solutions of the diophantine equation (x²+3x+1)²-33y²=-32.