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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 9 months ago

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

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

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

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`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

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Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

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

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

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

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