Question

What is the Tamil meaning for Butta bimmma?

Answer 1

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$p = 2$ & $p \equiv 1 \mod{4}$ & $p \equiv 3 \mod{4}$\\

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$p=2$ is clearly the sum of two squares, because $2 = 1^2 + 1^2$.

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&

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It can be demonstrated that $p$ is always the sum of two squares.

For example if $p$ is $5$ we have $5 = 1^2 + 2^2$.

If $p=13$ then $13 = 3^2 + 2^2$.

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&

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$p$ can never be the sum of two squares.

This is because a square number is congruent to $0$ or 1 modulo 4.

Hence the sum of two squares is congruent to $0$, $1$ or 2.

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Answer 2

Answer:

புட்டா பிம்மா

Explanation: