For an even perfect number n > 6, show the following:(a) The sum of the digits of n is
Chapter 11, Problem 1(choose chapter or problem)
For an even perfect number n > 6, show the following:(a) The sum of the digits of n is congruent to 1 modulo 9.[Hint: The congruence 26 = 1 (mod 9) and the fact that any prime p ::=::: 5 is of theform 6k + 1 or 6k + 5 imply that n = 2P-1(2P - 1) = 1 (mod 9).](b) The integer n can be expressed as a sum of consecutive odd cubes.[Hint: Use Section 1.1, l(e) to establish the identity below for all k ::=::: 1:13 + 33 + 53 + ... + (2k - 1)3 = 22k-2(22k-1 - l).]
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