Reply to Re: I gave up to the Computers National Olimpiad
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We had 3 hours. It wasn't that hard because it wasn't the national olympiad, it was just an inter-county contest.
I'll have the national olympiad on 17, this month.
For question 4, that was a nice observation, but did you managed to solve the problem using it?
For question 2, I'll tell you my ideea:
m=1: F is obviously surjective.
If m!=1, all we have to do is finding a matrix A that can't be equal with X^m, no mather what X is.
I think all the singular matrix have this property, but I'm not sure. For this question it's enough if we find one. So let's take A=((0,1),(0,0)).
I think it's elementary to prove that X^m=A has no solutions in M2(C).
I'll have the national olympiad on 17, this month.
For question 4, that was a nice observation, but did you managed to solve the problem using it?
For question 2, I'll tell you my ideea:
m=1: F is obviously surjective.
If m!=1, all we have to do is finding a matrix A that can't be equal with X^m, no mather what X is.
I think all the singular matrix have this property, but I'm not sure. For this question it's enough if we find one. So let's take A=((0,1),(0,0)).
I think it's elementary to prove that X^m=A has no solutions in M2(C).
