求方程3x²+5y²=345的正整数解
3x²=5(69-y²)
设：x=5x'
15x'²=69-y²
y²=3(23-5x'²)
设：y=3y'
3y'²=23-5x'²
5x'²+3y'²=23
x'=2,y'=1
x=10,y=3