## Pandigital | Pell equation : x^2 – k*y^2 = 1

Paul found :

$9801^2 \; - \; 725\times 364^2 \; = \; 1$

$458^2 \; - \; 209763\times 1^2 \; = \; 1$

$728^2 \; - \; 6543\times 9^2 \; = \; 1$

$30769208^2 \; - \; 5651487\times 12943^2 \; = \; 1$

$21543049^2 \; - \; 6893776\times 8205^2 \; = \; 1$

Now, can you find a pandigital solution to    $x^2 \; - \; k \, y^2 \; = \; m$

the digits of the combined integers (x, k, y, m) contain all digits from 0 to 9 (or 1 to 9)

math grad - Interest: Number theory
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### 3 Responses to Pandigital | Pell equation : x^2 – k*y^2 = 1

1. paul says:

Up to now I can only find a 1-9 solution

728^2 – 6543 * 9^2 = 1
P.

2. paul says:

Here is a 2 lots 0 – 9 pandigital

21543049^2 – 6893776 * 8205^2 = 1

P