Sunday, Nov 27, 2022

# Formula that captivated Ramanujan found

## A puzzle that caught the attention of Ramanujan seems to have become a little more clear.

Maths buffs rejoice! A puzzle that caught the attention of the legendary Indian scientist Srinivasa Ramanujan seems to have become a little more clear,thanks to a new study.

Ramanujan was captivated by the puzzle of how many ways a number can be created by adding together other numbers  a partition of a number is any combination of integers that adds up to that number.

For instance,4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1,so the partition number of 4 is 5. However,it becomes more complex with larger numbers and many mathematicians have struggled to find a formula for calculating it.

Ramanujan developed an approximate formula in 1918,which helped him spot that numbers ending in 4 or 9 have a partition number divisible by 5,and he found similar rules for partition numbers divisible by 7 and 11.

He offered no proof but said that these numbers had “simple properties” possessed by no others.

Now Ken Ono at Emory University in Atlanta,Georgia,and his colleagues have developed a formula that spits out the partition number of any integer.

They found “fractal” relationships in sequences of partition numbers of integers that were generated using a formula containing a prime number.