how many positive integers n are there such that both n and n+99 are perfect squares?
參考答案:n=x^2
n+99=y^2
so: y^2-x^2=(y+x)(y-x)=99
for:99=9*11,3*33,1*99
=> x=1,y=10
or x=15,y=18
or x=49,y=50
so: n=x^2=1,225,2401
=> there are 3 those integers
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how many positive integers n are there such that both n and n+99 are perfect squares?
參考答案:n=x^2
n+99=y^2
so: y^2-x^2=(y+x)(y-x)=99
for:99=9*11,3*33,1*99
=> x=1,y=10
or x=15,y=18
or x=49,y=50
so: n=x^2=1,225,2401
=> there are 3 those integers