2*m^z - m^z = ?

• To: mathgroup at smc.vnet.net
• Subject: [mg88104] 2*m^z - m^z = ?
• From: Alexey Popkov <popkov at gmail.com>
• Date: Fri, 25 Apr 2008 05:26:33 -0400 (EDT)

```Hello,

Table[
{2*m^z - m^z,
FullSimplify[2*m^z - m^z]},
{m, 1, 21}] // TableForm

The answer is very interesting (only odd numbers are treated well):

1					1
-2^z + 2^(1 + z)			2^z
3^z					3^z
2^(1 + 2*z) - 4^z			4^z
5^z					5^z
2^(1 + z)*3^z - 6^z		2^(1 + z)*3^z - 6^z
7^z					7^z
2^(1 + 3*z) - 8^z			8^z
9^z					9^z
2^(1 + z)*5^z - 10^z		2^(1 + z)*5^z - 10^z
11^z					11^z
2^(1 + 2*z)*3^z - 12^z		2^(1 + 2*z)*3^z - 12^z
13^z					13^z
2^(1 + z)*7^z - 14^z		2^(1 + z)*7^z - 14^z
15^z					15^z
2^(1 + 4*z) - 16^z		16^z
17^z					17^z
2^(1 + z)*9^z - 18^z		2^(1 + z)*9^z - 18^z
19^z					19^z
2^(1 + 2*z)*5^z - 20^z		2^(1 + 2*z)*5^z - 20^z
21^z					21^z

Can anyone explain the reason for this behavior?

```

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