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# Internal points

How many points strictly lie inside $$x^2$$ +$$y^2$$ = 25 such that both their x and y co-ordinates are non-zero integers

Note by Gautam Arya
3 weeks, 4 days ago

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See this article, then answer is $$N\left( \sqrt{25} \right) = 81$$.

- 3 weeks, 3 days ago

If I am not wrong, have you considered boundary points as well?

- 3 weeks, 2 days ago

Whoops, you're right! The revised answer should be $$81-12= 69$$. Because there are 12 boundary points: $$(0,0) , (\pm 5, 0 ) , (0, \pm 5) , (\pm3, \pm 4), (\pm4, \pm 3) , (\pm 3, \mp 4), (\pm 4, \mp 3)$$.

- 3 weeks, 2 days ago