Math Is Fun Forum

ryanjaberan

Novice

Registered: 2025-01-12

Posts: 1

Exercise

What is the smallest positive integer that has to be added with (1^14 + 2^14 + 3^14 +
⋯ +2024^14) so that the sum is divisible by 7?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,654

Re: Exercise

hi ryanjaberan

Welcome to the forum.

This problem has taken me back 53 or so years.  Had to rework some formulas.

I think the answer is

If that's correct then I'll post my method. If it's not, break it to me gently.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,899

Re: Exercise

Hi Bob;

Yes, I got that answer too...with a 27-character Mathematica formula using Sum & Mod that also runs in WolframAlpha.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,654

Re: Exercise

hi Phro, Thanks for that confirmation.  Here's my method:

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,899

Re: Exercise

Hi Bob;

Thanks for your method...I'll have to look at it tomorrow (bed now).

But before I go, here's my method:

Last edited by phrontister (2025-01-15 08:43:30)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson