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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-pell14qr | Structured version Visualization version Unicode version |
Description: Define the positive solutions of a Pell equation. (Contributed by Stefan O'Rear, 17-Sep-2014.) |
Ref | Expression |
---|---|
df-pell14qr | Pell14QR ◻NN |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpell14qr 37403 | . 2 Pell14QR | |
2 | vx | . . 3 | |
3 | cn 11020 | . . . 4 | |
4 | csquarenn 37400 | . . . 4 ◻NN | |
5 | 3, 4 | cdif 3571 | . . 3 ◻NN |
6 | vy | . . . . . . . . 9 | |
7 | 6 | cv 1482 | . . . . . . . 8 |
8 | vz | . . . . . . . . . 10 | |
9 | 8 | cv 1482 | . . . . . . . . 9 |
10 | 2 | cv 1482 | . . . . . . . . . . 11 |
11 | csqrt 13973 | . . . . . . . . . . 11 | |
12 | 10, 11 | cfv 5888 | . . . . . . . . . 10 |
13 | vw | . . . . . . . . . . 11 | |
14 | 13 | cv 1482 | . . . . . . . . . 10 |
15 | cmul 9941 | . . . . . . . . . 10 | |
16 | 12, 14, 15 | co 6650 | . . . . . . . . 9 |
17 | caddc 9939 | . . . . . . . . 9 | |
18 | 9, 16, 17 | co 6650 | . . . . . . . 8 |
19 | 7, 18 | wceq 1483 | . . . . . . 7 |
20 | c2 11070 | . . . . . . . . . 10 | |
21 | cexp 12860 | . . . . . . . . . 10 | |
22 | 9, 20, 21 | co 6650 | . . . . . . . . 9 |
23 | 14, 20, 21 | co 6650 | . . . . . . . . . 10 |
24 | 10, 23, 15 | co 6650 | . . . . . . . . 9 |
25 | cmin 10266 | . . . . . . . . 9 | |
26 | 22, 24, 25 | co 6650 | . . . . . . . 8 |
27 | c1 9937 | . . . . . . . 8 | |
28 | 26, 27 | wceq 1483 | . . . . . . 7 |
29 | 19, 28 | wa 384 | . . . . . 6 |
30 | cz 11377 | . . . . . 6 | |
31 | 29, 13, 30 | wrex 2913 | . . . . 5 |
32 | cn0 11292 | . . . . 5 | |
33 | 31, 8, 32 | wrex 2913 | . . . 4 |
34 | cr 9935 | . . . 4 | |
35 | 33, 6, 34 | crab 2916 | . . 3 |
36 | 2, 5, 35 | cmpt 4729 | . 2 ◻NN |
37 | 1, 36 | wceq 1483 | 1 Pell14QR ◻NN |
Colors of variables: wff setvar class |
This definition is referenced by: pell14qrval 37412 |
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