Valentine's Day Special - A Mathematical Aphrodisiac

Come Valentine's Day a lot of things happen around you. On one side one can see young men and women doing really crazy things to express their 'love'. While on the other side self-appointed policemen of culture, tradition etc come out with lathis and unleash terror. This is also the season when business heats up, specially for flower shops, greeting card, gift articles and so on. And the ubiquitous media does a good coverage of all these. When all the world is whirling with activity there is one category of people which doesn't seem to do much - the mathematicians. Mathematics is often perceived as a boring subject and mathematicians are often characterized as lost in their own proofs. Sometimes mathematicians can be interestingly romantic as well.

I recently read Simon Singh's Fermat's Last Theorem, an engrossing read. A simple adaptation from this book. There are something called friendly numbers. That sounds interesting. What are such numbers? There are some pairs of numbers which share an interesting relationship. When the sum of divisors of one number equals another number and vice versa then such a pair of numbers are called friendly numbers. Consider this example.

Divisors of 220 are 1,2,4,5,10,11, 20, 22, 44, 55 and 110. The sum of all these numbers is 284.

Divisors of 284 are 1, 2, 4, 71, 142. The sum of all these numbers is 220. 

This is a very special relationship. This kind of relationship doesn't happen with any pair of numbers in this world. This can happen only when a divine reason wants such a thing to happen. This relationship is something which doesn't wane with time but remains intact and even grows stronger. Doesn't this sound the way similar to the babble of a man bitten by some mad love bug? 

When Jacob met his angry
brother Esau, he gave 220 goats to
pacify him. It worked !!

When you ask the number 220, why it shares such a special relationship with 284 it may not babble anything like this. Unfortunately I am not a Number Theorist to hear and understand the romantic poems that 220 and 284 exchange. But this is an interesting mathematical fact.

With the Valentine's day around the corner, lovers have kick-started a maddening search for newer and more novel ways to express their love. Well this is the aphrodisiac that mathematics has on offer. But how?? Well you may give your beloved 284 roses and he may give you back 220 kisses.. That could be terrible. Anyways that is none of my business. 

For those who think friendly numbers are very small in size here is a brief list of other bigger friends pairs

• 1,184 and 1,210
• 17,296 and 18,416
• 9,363,584 and 9,437,056   

It is a very good thing to find young men and women searching for novel ways of expressing the love they have for one another. But this recent phenomenon of Valentine's Day appears to me more of a marketing trick. Some florists and card makers wanted to increase the sales. Somehow they found some nondescript saint who died many decades back and resurrected him. Hence Valentine's Day was born.

The best way to express one's love is just to love and keep loving through the thick and thin of times. Nothing much will ever be needed.