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Chris labels every lattice point in the coordinate plane with the square of the distance from the point to the origin (a lattice point is a point such that both of its coordinates are integers). How many times does he label a point with the number 25?

 Jan 21, 2021
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the equation for this is x^2+y^2=25 and when you solve for x and y 0, 1, 2, 3, 4 and 5 work. I think all of them work for x but for y only 0, 3, 4, and 5 work. what the two lists have in common is the numbers 0, 3, 4, 5 so the solutions can be (0, 3), (3, 4), (4, 5), (3, 5), (0, 4), and (0, 5) and all of their inverses. (an inverse means the negative of the number, e.g. the inverse of 3 is -3). The inverse works becase if you multiply the same negative twice, it becomes positive. (aka -x*-x=y, where x is negative). Remember, the equation is x^2+y^2=25 and a negative squared is positive. 

 

since there are 6 positive solutions as said above, all of them have a inverse so the answer is 6+6=12 times I think

 

not sure if this is correct tho

 Jan 21, 2021
edited by KitSoundwave  Jan 21, 2021
edited by KitSoundwave  Jan 21, 2021
edited by KitSoundwave  Jan 21, 2021
edited by KitSoundwave  Jan 21, 2021

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