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Can you solve these Number Theory problems in 30 seconds & 1 minute?

If possible, list all the solutions in limited time too!

You have 30 seconds for solving these problems.

Def: Lattice point is the point \((x,y)\) such that both \(x\) and \(y\) are integers.

1.) Find the number of lattice points of a hyperbola given by an equation

\[4x^{2}-y^{2}-2y-2558 = 0\]

2.) Find the number of lattice points of an ellipse given by an equation

\[2x^{2}-xy+2y^{2}+3x-3y-3 = 0\]


You have 1 minute for solving these problems.

1.) Find the number of ordered pair \((x,y)\) in integers of the equation

\[x^{2} - y! = 2559\]

2.) Find the number of ordered triples \((x,y,z)\) in integers of the equation

\[x^{2}+y^{2}+z^{2} = 2558xyz\]


Sometimes the math competitions in my country are too goddamn crazy. I hate it, and I'll never have this competition again. XD

Note by Samuraiwarm Tsunayoshi
1 year, 9 months ago

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