Math Problems

(Difference between revisions)
Revision as of 21:28, 24 Sep 2005
WikiSysop (Talk | contribs)
Initial.
← Go to previous diff
Current revision
Zeno (Talk | contribs)
Number theory
Line 16: Line 16:
=== Number theory=== === Number theory===
<ul> <ul>
- <li> Determine the number of odd numbers in the nth row of pascal's triangle. </li>+ <li> Determine the number of odd numbers in the nth row of Pascal's triangle. </li>
- <li> Determine which rows of pascal triangle contain an arithematic progression, a,a+b,a+b+b. </li>+ <li> Determine which rows of Pascal's triangle contain an arithematic progression a,a+b,a+b+b. </li>
- <li> Show that the fibonacci numbers have the property, + <li> Show that the Fibonacci numbers have the property,
f(gcd(m,n))=gcd(f(m),f(n)). f(1)=f(2)=1,f(n+2)=f(n+1)+f(n). <em> by Polytope </em> </li> f(gcd(m,n))=gcd(f(m),f(n)). f(1)=f(2)=1,f(n+2)=f(n+1)+f(n). <em> by Polytope </em> </li>
<li> If C(n) is a sequence of non-zero integers such that gcd(C(m),C(n)) = <li> If C(n) is a sequence of non-zero integers such that gcd(C(m),C(n)) =
Line 24: Line 24:
C(n) C(n-1) ... C(n-k+1) / C(k) C(k-1) ... C(1) ] are all integers. C(n) C(n-1) ... C(n-k+1) / C(k) C(k-1) ... C(1) ] are all integers.
<em> by Polytope, from Concrete Mathematics, Knuth, Graham, Patashnik. </em> </li> <em> by Polytope, from Concrete Mathematics, Knuth, Graham, Patashnik. </em> </li>
- <li> Show that the n'th fibonacci number is prime only if n=4 or n is prime. + <li> Show that the nth Fibonacci number is prime only if n=4 or n is prime.
Which Fibonacci numbers are prime? Are there infinitely many such primes? Which Fibonacci numbers are prime? Are there infinitely many such primes?
- <em> by Polytope (possibly open)</em> Note: The 9311th fibonacci number+ <em> by Polytope (possibly open)</em> Note: The 9311th Fibonacci number
is prime. </li> is prime. </li>

Current revision

These trivia questions and puzzles were taken from mowsey's original #math FAQ.

Table of contents

Trivia and Trivialities

Puzzles

Number theory

Enumerative combinatorics

Algebra


Analysis

Topology

Geometry

Statistics

TeX