James Wanless on Wed, 28 Apr 2010 13:22:00 +0200

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 Re: Big number division bug?

```Aha!
Thanks very much to both Karim and Robert...
```
I was (previously) unaware I was repeating factors (stupidly :) - should have tested them for primailty... and so was expecting the last result to be zero too.
```Thanks again very much for your prompt and informative replies
J

On 28 Apr 2010, at 11:57, Karim Belabas wrote:

```
```* James Wanless [2010-04-28 12:41]:
```
```I don't know if PARI is intended to handle such big numbers, but:

? (2^43112609+1)%(3*86225219*5259738299*5949540043)
%1 = 0
? (2^43112609+1)%12482997260297
%2 = 0
? (2^43112609+1)%453522086713962481
%3 = 0
```
? (2 ^ 43112609 + 1 ) %(3*86225219*5259738299*5949540043*12482997260297*453522086713962481)
```%4 = 20781231343178972948687277924200040219405288340527425880342

[GMP-ECM shows the same problem, so I don't know if it could even be
a bug in GMP???]
```
```
I do not see a problem there : your moduli are not coprime
```
( in fact, 453522086713962481 divides 3*86225219*5259738299*5949540043)
```so you can't deduce that the result should be 0 by the CRT.

What result were you expecting ?

Cheers,

K.B.

P.S: The result given is consistent with the output of
```
N = 3*86225219*5259738299*5949540043*12482997260297*453522086713962481
```  lift( Mod(2,N)^43112609 + 1 )
which handles only tiny integers.

--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~belabas/
```
F-33405 Talence (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]
````
```
```

```