HOW?! "State any points on each curve whose coordinates are both integers"

(a) #x^2 + y^2 = 5#

1 Answer
Ananda Dasgupta
Mar 15, 2018

#(1,2),(-1,2),(1,-2),(-1,-2),(2,1),(-2,1),(2,-1),(-2,-1)#

Explanation:

The only pair of positive integers whose squares add up to 5 are 1 and 2. (since #2^2+2^2# is already more than 5, there is no need to look any further). These could be either the #x# or the #y# coordinate. On top of this, one, or both, of the coordinates may change sign.

The coordinates can thus be

#(1,2),(-1,2),(1,-2),(-1,-2),(2,1),(-2,1),(2,-1),(-2,-1)#

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