# re: special math characters

OK, this is not good news, but at least there is a fix.

The problem has to do with the special database encoding that is needed to make these special characters work. It was set up correctly on the old server, and for some reason I thought, or rather imagined, that it would work well on the new server. More work will have to be done to fix it. However, having done it once – in the distant past – I can figure out how to do it again.

Thanks for letting me know.

### figures

Dear unlord,

It’s nice to hear that there exists a solution to that character problem. Of course there are here other, bigger problems – one of the hardest ones is perhaps formed by the figures (graphs etc.) in the PlanetMath articles.

### Math special characters

Hi unlord,

I have found a partial solution to the problem concerning the math fraktur letters in the PM articles: Remove from the LaTeX-form text the expressions containing thmplain, PMlinkescapeword, PMlinkname. Then the fraktur letters are visible. The same concers probably the math calligraphy letters.

A new(?) problem may be that the autolinking works nowadays quite poorly.

Is there any knowledge on the final great rebuilding of PlanetMath? Many persons are waiting it.

Regards,

Jussi

### Fermat's theorem in Z(i) (contd)

Program in pari for generating Gaussian integer quotients - an example: p(n) = ((n + I)^12-1)/13. This, of course, fails when n is such that (n + I) is not coprime with the prime factors of 13 in Z(i).

### A property of polyomials

Let us, for the present, confine ourselves to the ring of integers. Sometime ago I had stated that the following property of polynomial holds: let f(x) be a polynomial ring,where x belongs to Z. Let x_0 be a specific value of x.. Then f(x_0 + k*f(x_0)) is congruent to 0 (mod f(x_0). Here k belongs to N. Now it looks as if f(x_0 + k*f(x_0)) is also congruent to f(x_0+1), in the case of monic polynomials only.

### A property of polyomials (contd)

Apparently this property is exhibited by monic polynomials in Z(i) too.

### A property of polynomials (contd)

This property is exhibited by monic polynomials in Z where the variable is a square matrix in which each element belongs to Z.

### A property of polyomials (concluding).

Let f(x) be a monic polynomial. Then a) f(x_0 +k*f(x_0)) is congruent to 0 mod (f(x_0)) b) it is also congruent to 0 mod(f(x_0+1) c) It is also congruent to 0 mod(x_0 + i) in the case when x is a Gaussian integer and d) it is also congruent to 0 mod (f(x_0) and mod(f(x_0 + 1) when x is a square matrix in which each element belongs to Z(i). Here k belongs to N.