split - Happy new year 2019 digit problem

[crocoyes1]

The number 2019 can be written as the sum of the first n perfect powers (integers of the form am where a>0 and m≥2). What is the value of n?

 

[Deleted member 4993]

The number 2019 can be written as the sum of the first n perfect powers (integers of the form am where a>0 and m≥2). What is the value of n?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this assignment.

 

[Dr.Peterson]

The number 2019 can be written as the sum of the first n perfect powers (integers of the form a^m where a>0 and m≥2). What is the value of n?

I would just start listing perfect powers, and start adding. At the very least, this will help you understand what the claim is; and if it looks like n will be too large to find by actually adding, you'll be gaining knowledge of how the problem works, that might lead to seeing a shortcut.

I'd probably do this with a spreadsheet.

By the way, I think the intention was to require a and m, not just a^m, to be integers.

 

[JayJay]

How do we treat a number such as 64, both a square and a cube? Would it be included in the total just once or twice? If twice, how do we treat the higher powers of 1?

 

[Dr.Peterson]

How do we treat a number such as 64, both a square and a cube? Would it be included in the total just once or twice? If twice, how do we treat the higher powers of 1?

That's for you to decide, as the problem is not clearly stated, and only you know the context (because you didn't follow our guidelines).

But I would count each distinct number once.

 

[JayJay]

That's for you to decide, as the problem is not clearly stated, and only you know the context (because you didn't follow our guidelines).

But I would count each distinct number once.

Not my problem. I'm just trying to help the OP.
I cannot see how a spreadsheet could be set up to solve this.

 

[Dr.Peterson]

Sorry, you wrote as if you were the OP, and I didn't check who you are. It's theirs to decide.

A spreadsheet is only a way to list the numbers easily. I don't think there's any "mathematical" way to answer it, because a formula would be too complex. I have found the answer by spreadsheet, using several manual steps.