If n is prime, the Legendre symbol of a∈ℤ is written (a/n) and defined by:
⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ | = | ⎧ ⎪ ⎨ ⎪ ⎩ |
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The Legendre symbol satisfies the following properties.
⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ | . | ⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ | =(−1) |
| .(−1) |
| , | ⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ | =(−1) |
| , | ⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ | =(−1) |
| . |
The legendre_symbol command computes the Legendre symbol.
legendre_symbol(26,17) |
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legendre_symbol(27,17) |
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legendre_symbol(34,17) |
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