Leesajohnson* is probably not a bot. This person put a advert for tutoring services in their signature, which I removed. The administrators and moderators have discussed this growing problem but decided not to ban automatically but rather to remove the advert and wait to see what the member does next.

Some ago a person joined to tell us about some new mathematical research they had done and included a link to their book sale page. The work was genuine but the advert broke our rules. The person agreed to make a pdf of their work available to MIF members for free and that seemed to be a good compromise.

Some cases are hard to determine such as the recent bit coin maths puzzle post. Do I want to seem to encourage bit coin? But the puzzle was one that members might want to try. So I deleted the link but kept the puzzle.

Bob

ps. * Also I noticed 6 English grammar and spelling faults in that post. What sort of advert is it when the 'tutor' cannot write good English?

Make a habit of study

ingmathand thiswill make you proficient in this subject. It is good to studyfrombooks and get tuition from expert tutors,full stop / new sentence starting with 'This'is the indication ofreplace 'of' with 'for a'better future.pps. On the other hand if this is from a bot, then it's entirely appropriate to post it in 'computational math'.

Yes. I am wary of these suspicious people posting some psuedoadvertisements.

And so many [sic]s, making me [sic]!

pps. Hmmmm. Indeed.

I may have been a bit hasty when I wrote that. I meant to say a lot better.

And the truth shall set you free . . . good one!

]]>I do not understand what you want.

]]>```
SequenceLimit[{-0.5`, -0.5833333333333334`, -0.6345238095238095`, \
-0.6628718503718504`, -0.6777662022075269`, -0.685395708269249`, \
-0.6892561888834033`, -0.691197870228108`, -0.6921715717324427`, \
-0.6926591377284108`}]
```

The amount of math and other things stuffed into mathematica is unbelievable.

]]>Good to see you getting back into math and smart to use some modern tools like Geogebra to assist you.

]]>This problem appears in another thread and someone asked to see my solution.

1) Find a fifth degree polynomial f(x) with the conditions (x-1)^3 | f(x) -1 and x^3 | f(x).

The outline of how it is done.

We get the remainders:

Those remainders on the RHS must be set to 0 and the coeficients equated to 0.

From that we get 6 simultaneous equations that are easy to solve:

So the polynomial we seek is

Of course it is much easier using Mathematica:

Way 1:

```
p[x_, a_, b_, c_, d_, e_, f_] := a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f
rul = FindInstance[
ForAll[x,
PolynomialRemainder[p[x, a, b, c, d, e, f] - 1, (x - 1)^3, x] ==
0 && PolynomialRemainder[p[x, a, b, c, d, e, f], x^3, x] ==
0], {a, b, c, d, e, f}] // First;
p[x, a, b, c, d, e, f] /. rul // TraditionalForm
```

yields:

6 x^5-15 x^4+10 x^3

Way 2:

```
p[x_, a_, b_, c_, d_, e_, f_] :=
a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f;
PolynomialRemainder[p[x, a, b, c, d, e, f] - 1, (x - 1)^3, x];
PolynomialRemainder[p[x, a, b, c, d, e, f], (x)^3, x];
rul = Solve[{-1 + 6 a + 3 b + c + f == 0, (-15 a - 8 b - 3 c + e) ==
0, (10 a + 6 b + 3 c + d) == 0, f == 0, e == 0, d == 0}, {a, b,
c, d, e, f}][[1]];
p[x, a, b, c, d, e, f] /. rul
```

10 x^3 - 15 x^4 + 6 x^5

]]>