Introduction to Number Theory
نویسندگان
چکیده
This seems simple enough, but let’s play with this definition. The Pythagoreans, an ancient sect of mathematical mystics, said that a number is perfect if it equals the sum of its positive integral divisors, excluding itself. For example, 6 = 1 + 2 + 3and 28 = 1 + 2 + 4 + 7 + 14are perfect numbers. On the other hand, 10 is not perfect because 1 + 2 + 5 = 8, and 12 is not perfect because 1+2+3+4+6 = 16. Euclid characterized all the even perfect numbers around 300 BC. But is there an odd perfect number? More than two thousand years later, we still don’t know! All numbers up to about 10300 have been ruled out, but no one has proved that there isn’t an odd perfect number waiting just over the horizon.
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