## Related questions with answers

Question

Is conjecture $(1)$ in the text (that the $n$th perfect number contains exactly $n$ digits) true or false? Explain.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Conjecture (1) is false. According to the condition, the 5th perfect number should have 5 digits exactly but 33,550,336 is composed of 8 digits. Furthermore the 6th perfect number 8,589,869,056 has 10 digits.

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