nakamoto2305
New member
- Joined
- Jun 27, 2021
- Messages
- 7
Find the pair of positive integers [MATH]x,y[/MATH] such that [MATH]k[/MATH] is the smallest possible and [MATH](n^2+1)((n+k)^2+1)[/MATH] is a square number.
I can easily prove that [MATH]k[/MATH] must be an even number, and I also found out the answer is [MATH](n;k)=(1;6)[/MATH].
I can prove that with k=2, there is no solution, but I still confuse with k=4; btw, this way is not good because it looks like I guess the answer and just prove there is no solution for n with all value [MATH]k[/MATH] smaller than [MATH]6[/MATH] .
So I try another way that can prove clearly k=6 is the smallest that can give a solution for this problem, can u help me?
And sorry for my bad grammar.
I can easily prove that [MATH]k[/MATH] must be an even number, and I also found out the answer is [MATH](n;k)=(1;6)[/MATH].
I can prove that with k=2, there is no solution, but I still confuse with k=4; btw, this way is not good because it looks like I guess the answer and just prove there is no solution for n with all value [MATH]k[/MATH] smaller than [MATH]6[/MATH] .
So I try another way that can prove clearly k=6 is the smallest that can give a solution for this problem, can u help me?
And sorry for my bad grammar.