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Determine the smallest positive integer k such that \($60^n + k \cdot 71^n$\) is divisible by 1441 for all odd positive integers n.

 May 8, 2019
edited by mathhdude124  May 8, 2019
 #1
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k=1;n=1; a=if((60^n + k*71^n) %1441==0, goto3, goto4);printn; n++; k++;if(n<=1000, goto2, 0);if(k<1000, goto2, discard=0;

The smallest positive ineger for k = 263

 May 8, 2019
 #2
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Hi guest,

I find your little lines of code very interesting. 

I have checked your answer just for n=1 and it is certainly true.

 

But

I'd really like to see somone solve this one mathematically.

I started but got it wrong.  Maybe I just made a silly error or maybe I was on completely the wrong path.  frown

 May 9, 2019
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Hi Melody: Writing a very short line of code, like this one, is a trivial matter, but it finds the answer in milliseconds. I generally await somebody like yourself or one of the other mathematicians to flesh out the details of the problem using Algebra, Calculus, Trig,....etc. I have forgotten most of that stuff since taking them, when dinosaurs roamed the Earth!.

 May 9, 2019
edited by Guest  May 9, 2019
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Yes I understand that but I like that you are giving answers with your code that so far have shown to be correct.

It is like being given the answer from the back of the text book. I like that you are doing it.

Coding is something that I would like to study but there are so many things I want to study that I do not know if I wil ever get to it.

I have forgotten most of what I learned in the Jurassic period too  sad

Melody  May 9, 2019

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