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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 months, 3 weeks ago

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

Pi Han Goh - 3 months, 3 weeks ago

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

Gautam Arya - 3 months, 3 weeks ago

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

Pi Han Goh - 3 months, 3 weeks ago

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