Given two integers x,y>1. S knows s=x+y and P knows p=x y. We hear the dialog: P: ``I don't know x,y". S: ``I don't know x,y". P: ``I don't know x,y". S: ``I don't know x,y". P: ``I now know x,y". S: ``I now know x,y". What are the integers? t.co/2Bl2m8UmtD t.co/vLhUqWsVnr
Gogole generates Bach-inspired tunes with AI-powered Google doodle.
My test: t.co/RkhD1QK38A Pretty cool. A similar thing has been done by a student in a Math 21b mathematica project
who used a database of written poems to enhance a given one. t.co/0ekAlu6EUG
Special pi day today: 3/14/2019 as 3142019 is prime.
e^pi - pi^e = 0.68153 reminds of the golden ratio phi=1.61803. An identity to celebrate Pi Day: Pi^((E^Pi)^I)*Pi == 1.Picture:
n=100;MatrixPlot[Partition[IntegerDigits[Floor[(10^(n^2)) Pi],10],n]] t.co/Sry8mmvaKf
Nice fire pits allow to relax near the Science Center Plazza at Harvard. Behind, the staircase structure with floors 2,3,4 (first terrace with my office),5,6,7,8 and telescope. Perspective renders the floor levels appear non-parallel. Additional non-linear distortion due to heat. t.co/9SWbZ3WQ12
Cool n-body simulation in WebGL t.co/sD7qqH8tKL The database illustrates interest in asteriods, not only because of collision hazard. Look at all that dough lying around! 1.2 Trillion profit estimate for 20111 UW 158, 30 billion for Ryugu (just visited by Hayabusa)!Wow! t.co/Py09JJwrFw
Silverman 4x4 chess. Chess mate in 4 moves! Silver wins in at least 4 moves (see picture). Was used as a demonstration in 2007 t.co/W7jXoprekY. There is a 4-move chess mate solution which does not branch. Can you find it? (Play online at t.co/HuMEv2pXNG) t.co/82SpkMmI2W
The super queen problem asks to place n non-interacting queens which can attack also distance 3 or less t.co/UPxdblUeEL The solution is unique for n=10 up to rotation.Which is the smallest n for which super queen configurations are possible which can attack distance <k? t.co/mQzfHcWIJC
Wilson: (n-1)!+1 = 0 mod n <=> n prime
Fermat: a^n-a=0 mod n for all a if n is prime
Carmichael Fermat pseudo primes -> Miller-Rabin
Laisand-Beujeux (1879): B(p-1,k)=(-1)^k mod p for k=(p-1)/2 and prime p
t.co/0xQoV2Aw5k (Maheswara Valluri) Is 5907 only L-B pseudo prime? t.co/dnS9A3wBNG
One of the greatest mathematicians of our time died yesterday:
An older longer insightful interview with Michael Atiyah was just published on youtube t.co/YU6QpYkHjj
where also his discoveries with Singer are discussed. t.co/sgSlCUK2TR
My running route passes close to a golf course ...
How come Kepler always comes to mind? t.co/hbm5lXZeKA