- #1
firefly767
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this might be answered already, but i didnt find a detailed proof... so here it goes:
1. an integer n is perfect if the sum of its divisors including 1 and itself is 2n. show that if 2^p-1 is a prime number, then n=2^(p-1) (2^p -1) is perfect.
2. show that 1+ 1/2 + 1/3 +... +1/n can never be an integer if n>1.
3. if [x] is the greatest integer less than or equal to x, then for which values of n does [sqrt n] divide n?
1. an integer n is perfect if the sum of its divisors including 1 and itself is 2n. show that if 2^p-1 is a prime number, then n=2^(p-1) (2^p -1) is perfect.
2. show that 1+ 1/2 + 1/3 +... +1/n can never be an integer if n>1.
3. if [x] is the greatest integer less than or equal to x, then for which values of n does [sqrt n] divide n?