Mike Hirschhorn's simple proof of mod 11 congruence by Ramanujan translated into Spanish

Dr Mike Hirschhorn discovered a simple proof of the mod 11 congruence earlier this year.

His proof inspired an article by Edinah Gnang and Doron Zeilberger, which is set to appear in Spanish in the analog of the American Mathematical Monthly in Spain.

In 1917, Ramanujan discovered that if p(n) is the number of partitions of the number n, that p(11n+6) is divisible by 11.

For example, p(6)=11 since 6=5+1=4+2=4+1+1=3+3=3+2+1=3+1+1+1=2+2+2=2+2+1+1=2+1+1+1+1=1+1+1+1+1+1 (11 ways of writing 6 as a sum of weakly decreasing positive integers).

He also discovered that p(5n+4) is divisible by 5, and p(7n+5) is divisible by 7. He gave simple proofs of these two, but although he managed to prove the mod 11 congruence, his proof is difficult and deep, requiring considerable background.

English mathematician G. H. Hardy wrote “[the mod 11 congruence] is more difficult.'' Dr Hirschhorn claims that it has always been his goal to find a simple proof of the mod 11 congruence.