Amicable numbers

Project work

1. Amicable Numbers

2. How to find out pairs of Amicable Numbers One of the most beautiful concepts from maths constituts the “ Amicable Numbers” But what are ‘Amicable numbers’ ? DEFINITION: Each number is equal with the sum of the divizors of the other number including 1 and excluding the number itself (like divizors) Examples of amicable numbers: 220 and 284 , 1184 and 1210 , 2620 and 2924 .

3. The first amicable numbers were discovered in antiquity. Examples for finding out pairs of amicable numbers: D 220 ={1,2,4,5,10,11,20,22,44,55,110,220} 1+2+4+5+10+11+20+22+44+55+110= 284 D 284 ={1,2,4,7,71,142,284} 1+2+4+7+71+142= 220 => 220 and 284= amicable numbers

4. . D 1184 ={ 1,2,4,8,16,32,37,74,148,296,592 } 1+2+4+8+16+32+37+74+148+296+592=1210 D 1210 ={1,2,5,10,11,22,55,110,121,242,605} 1+2+5+10+11+22+55+110+121+242+605=1184 => 1184 and 1210= amicable numbers

5. PITAGORA was the first who discovered the first pair of amicable numbers [220 and 284] Much later, in 1636, PIERRE FERMAT discovered the second pair of amicable numbers (17296 and 18416)

6. BIBLIOGRAPHY http://desprenumere.blogspot.ro/2012/12numuere-prietene.html http://ro.wikipedia.org/wiki/Numere_prietene http://en.wikipedia.org/wiki/Amicable_numbers http://mathworld.wolfram.com/AmicablePair.html http://www.numbergossip.com/list#amicable_numbers