## La ricerca ha trovato 18 risultati

13 nov 2007, 16:46
Forum: Teoria dei Numeri
Argomento: sequence and powers
Risposte: 6
Visite : 3551

### sequence and powers

A prime number $p$ is given. A sequence of positive integers $a_{1},a_{2},a_{3},...$ is determined by this conditon:
$a_{n+1}=a_{n}+p \lfloor \sqrt[p]{a_{n}} \rfloor$
Prove that there is a term in this sequence, which is a $p$-power of an integer number.
04 nov 2007, 16:37
Forum: Algebra
Argomento: combinatorical problem with subsets
Risposte: 3
Visite : 3199

### combinatorical problem with subsets

There is integer number $x\geqslant 2$ . Find the smallest integer number$y\geqslant x$, such that for every division of set$\lbrace x, x+1, ..., y\rbrace$ into two subsets at least one of thease subsets contains such numbers $m, n, p$ (not necessarily different), such that $mn=p$ .
04 nov 2007, 14:55
Forum: Geometria
Argomento: una piramide e una sfera hanno iscritto
Risposte: 4
Visite : 4027
no one could do it?
15 ott 2007, 17:39
Forum: Geometria
Argomento: una piramide e una sfera hanno iscritto
Risposte: 4
Visite : 4027
no ideas at all?? I have one solution but it's horrible and I'll post it after someone else will prove this
15 ott 2007, 17:36
Forum: Algebra
Argomento: un insieme si è diviso in due sottoinsiemi
Risposte: 7
Visite : 4322
Now I know this solution is wrong. Cause n must be related to m (which is given)
So if someone has any solution please post it!
11 ott 2007, 22:12
Forum: Algebra
Argomento: un insieme si è diviso in due sottoinsiemi
Risposte: 7
Visite : 4322
I have the same but i'm not sure if it's correct
11 ott 2007, 21:31
Forum: Algebra
Argomento: Diseguaglianza a + b + c = 3
Risposte: 8
Visite : 4758
Could you show how you've got a = b ?? I dont know what CM and AM are.
11 ott 2007, 21:12
Forum: Algebra
Argomento: un insieme si è diviso in due sottoinsiemi
Risposte: 7
Visite : 4322
reals but total {-1,-2,1,5, etc.}
11 ott 2007, 20:34
Forum: Geometria
Argomento: una piramide e una sfera hanno iscritto
Risposte: 4
Visite : 4027

### una piramide e una sfera hanno iscritto

A pyramid $ABCDS$ is given (the base is convex quadrilateral). A sphere is inscribed in this pyramid and it is tangent to side ABCD at point P.
Prove that
$\angle APB + \angle CPD = 180^{o}$
11 ott 2007, 19:50
Forum: Algebra
Argomento: Diseguaglianza a + b + c = 3
Risposte: 8
Visite : 4758
but why is a=b?? Could you explain?
11 ott 2007, 12:55
Forum: Algebra
Argomento: un insieme si è diviso in due sottoinsiemi
Risposte: 7
Visite : 4322

### un insieme si è diviso in due sottoinsiemi

We have a total number $m \geq 2$ We must find the smallest total number n which is:
$n \geq m$
and for which:

for all divisions of the set {m, m+1, ..., n} into two subsets at least one of the subsets contains such number a, b, c (not necessary different)
that ab = c
10 ott 2007, 19:36
Forum: Geometria
Argomento: Punti su un triangolo
Risposte: 1
Visite : 2308

### Punti su un triangolo

Points $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6}, P_{7}$ are placed correspondingly on sides $BC, CA, AB, BC, CA, AB, BC$ of triangle $ABC$ and thease angles are equal:
$P_{1}P_{2}C = AP_{2}P_{3} = P_{3}P_{4}B = CP_{4}P_{5} = P_{5}P_{6}A = BP_{6}P_{7} = 60^{o}$
Prove that
$P_{1} = P_{7}$
10 ott 2007, 19:20
Forum: Algebra
Argomento: Diseguaglianza a + b + c = 3
Risposte: 8
Visite : 4758
I know that the answer is -5 but can't prove it
10 ott 2007, 18:35
Forum: Algebra
Argomento: Diseguaglianza a + b + c = 3
Risposte: 8
Visite : 4758

### Diseguaglianza a + b + c = 3

Find the smallest real number x , such that: For arbitrary real numbers $a, b, c \geqslant x$ and $a + b + c = 3$ this inequality is correct:$a^{3} + b^{3} + c^{3} \geqslant 3$
10 ott 2007, 14:17
Forum: Combinatoria
Argomento: mundial e per la matematica
Risposte: 12
Visite : 7775
So any ideas so far? I know a bit itallian but i prefer english. I havent't noticed too many people speaking english on OliForum