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# Z^Z|=Z^2 find all integer roots. Z is not 0

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Director
Joined: 26 Feb 2006
Posts: 905
Followers: 4

Kudos [?]: 52 [0], given: 0

Z^Z|=Z^2 find all integer roots. Z is not 0 [#permalink]  13 May 2007, 22:54
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|Z^Z|=Z^2 find all integer roots. Z is not 0.
Intern
Joined: 29 Jan 2007
Posts: 17
Followers: 0

Kudos [?]: 1 [0], given: 0

Sergey_is_cool wrote:
I got 1, -1, and 2

I don't agree with -1.

-1^-1 = - 1/10 => 1/10
-1^2= 1

Therefore it is only 1 and 2.
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

transatlantiker wrote:
Sergey_is_cool wrote:
I got 1, -1, and 2

I don't agree with -1.

-1^-1 = - 1/10 => 1/10
-1^2= 1

Therefore it is only 1 and 2.

-1 is in too

If Z=-1, then
o |Z^Z|= |(-1)^-1| = |1/(-1)| = |-1| = 1
o Z^2 = (-1)^2 = 1

So, |Z^Z| = Z^2
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

transatlantiker wrote:
Fig wrote:
transatlantiker wrote:
Sergey_is_cool wrote:
I got 1, -1, and 2

I don't agree with -1.

-1^-1 = - 1/10 => 1/10
-1^2= 1

Therefore it is only 1 and 2.

-1 is in too

If Z=-1, then
o |Z^Z|= |(-1)^-1| = |1/(-1)| = |-1| = 1
o Z^2 = (-1)^2 = 1

So, |Z^Z| = Z^2

You are right... I was stupid. THX.

You are not right ... U are not stupid (just a mistake )... U are welcome
Director
Joined: 26 Feb 2006
Posts: 905
Followers: 4

Kudos [?]: 52 [0], given: 0

Fig wrote:
transatlantiker wrote:
Fig wrote:
transatlantiker wrote:
Sergey_is_cool wrote:
I got 1, -1, and 2

I don't agree with -1.

-1^-1 = - 1/10 => 1/10
-1^2= 1

Therefore it is only 1 and 2.

-1 is in too

If Z=-1, then
o |Z^Z|= |(-1)^-1| = |1/(-1)| = |-1| = 1
o Z^2 = (-1)^2 = 1

So, |Z^Z| = Z^2

You are right... I was stupid. THX.

You are not right ... U are not stupid (just a mistake )... U are welcome

you are right .................he/she is not..................
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