A perfect square is a number of the form N = x^2, where x is an integer. Solitary numbers are numbers which are not friendly. Friendly numbers, on the other hand, are numbers which constitute a friendly pair (m, n), where sigma(m)/m = sigma(n)/n and sigma is the sum-of-all-positive-divisors function. You can refer to the MathWorld pages for Friendly and Solitary Numbers for more information. From the MathWorld initial list of solitary numbers, it appears that 1, 4, 9, 16, ... are all solitary. Can you prove that all perfect squares are solitary?
2007-05-25
12:05:59
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2 answers
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asked by
JoseABDris
2
in
Mathematics