       PowerMod[] - Mathematica 5.0 - problem/error/bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg73029] PowerMod[] - Mathematica 5.0 - problem/error/bug?
• From: Anton Vrba <antonvrba at yahoo.com>
• Date: Tue, 30 Jan 2007 06:36:13 -0500 (EST)

```In Mathematica 5.0 I found on my system the following incorrect result regarding the PowerMod[] function

You agree that PowerMod[2,17 p, p]=2^17 for p prime and p>2^17

Mathematica 5.0 calculates PowerMod[2,17 p, p] as 2^2
for p=126322571 through to p=2147483647. (one can change the 2 to any base and the wrong answer base^2 is calculated)

below the notebook file converted to text format.

Have I a problem in my system? or is this a Mathematica 5.0 bug or possibly a new Pentium bug?

best regards
Anton

In:=
p=Prime
y=PowerMod[2,17  p,p]
FactorInteger[y]
"y is the correct result"

p=Prime
y=PowerMod[2,17  p,p]
FactorInteger[y]
"y should equal 2^17 and not 2^2"

m=5
y=PowerMod[2,(2^(32 m)-1)  p,p]
FactorInteger[y]
m=12
y=PowerMod[2,(2^(32 m)-1)  p,p]
FactorInteger[y]
"y equal 2^(m+1) is a cute result"

Out=2543568329
Out=131072
Out={{2,17}}
Out=y is the correct result
Out=2112226087
Out=4
Out={{2,2}}
Out=y should equal 2^17 and not 2^2
Out=5
Out=64
Out={{2,6}}
Out=12
Out=8192
Out={{2,13}}
Out=y equal 2^(m+1) is a cute result

In:=
"here is the range of the error"
p=Prime
FactorInteger[PowerMod[2,17  p,p]]
p=Prime[7181138+1]
FactorInteger[PowerMod[2,17  p,p]]
p=Prime
FactorInteger[PowerMod[2,17  p,p]]
p=Prime[105097565+1]
FactorInteger[PowerMod[2,17  p,p]]
Out=here is the range of the error
Out=126322543
Out={{2,17}}
Out=126322571
Out={{2,2}}
Out=2147483647
Out={{2,2}}
Out=2147483659
Out={{2,17}}

```

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