The number 4 can be partitioned in 5 ways. 1+1+1+1+1, 2+1+1, 2+2, 3+1, and 4. The number 9 can be partitioned in 30 ways and 14 in 135 ways. In fact, any number ending in 4 or 9 can be partitioned in x ways, where x is divisible by 5. The numbers 4, 9, and 14 are said to be congruent to each other.
This mathematical pattern has been observed by the genius Srinivasa Ramanujan decades ago. He found partition congruences for 5, 7 and 11. Recently, Karl Mahlburg, a PhD student at the University of Wisconsin in Madison, USA, generalized this theory on partition congruences. The new scientist magazine reports that his results have applications in particle physics and computer security.
Subscribe to:
Post Comments (Atom)
-
We wished to have our own home for a long time. Late last year, we finally started building one. The groundbreaking went without fanfare.... -
Noong unang panahon, sa konstantinopla Hari ang pipino, reyna ang malunggay May anak-anakan na isang prinsesa Bansag na pangalan, si don...
-
During the early nineties, I was involved in the Fractal Image Compression research of Ateneo de Manila. Last night, I uncovered an early I...
1 comment:
people with too much time on their hands...hehehe
Post a Comment