Enter a numerical palindrome (sequence of positive natural numbers separated by spaces)
Receive the polynomial that gives all possible n ∈ N such that the continued fraction of √n starts with [z, «palindrome», 2z] for some z
«Your polynomial will display here»
How to use this calculator
- Choose a palindrome (ex.: "3 4 1 4 3" or "2 13 13 2")
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If it has even length
- Enter the first half (2 13 13 2)
- Leave "Middle element" blank
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If it has odd length
- Enter the elements before the middle (3 4 1 4 3)
- Enter the middle element (3 4 1 4 3)
- Click Calculate to get the polynomial
How polynomials are calculated
Palindrome to polynomial mapping:
| Palindrome | Polynomial | |
| [ ] (Empty) | f(x) = x2 + 1 | x ∈ N |
| [2m] | f(x) = (m2x + 1)x | x > 0 |
| [2m − 1] | f(x) = ((2m − 1)2x + 2) | x > 0 |
| [1, 2m − 1, 1] | f(x) = ((2m + 1)2x + (2m + 1)2 − 2)(x + 1) | x ∈ N |
For the other cases, read the paper