0
$\begingroup$

Let's have the following numbers.

34932, 52428, 10023, 1881, 512, 64764, 63012, 57825, 59367, 65508, 30840, 55449, 18009, 65537, 20148, 39321, 62361, 27756.

  1. What are the relations between these numbers.

  2. How have these numbers been created?

HINT:

Think Pythagoras

$\endgroup$
8
  • 11
    $\begingroup$ If you multiply each of them by zero you get zero as a result $\endgroup$
    – PDT
    Aug 23, 2020 at 21:14
  • 3
    $\begingroup$ Ι never looked at it that way. You are miles away from the answer. $\endgroup$ Aug 23, 2020 at 21:48
  • 4
    $\begingroup$ It was a joke mate $\endgroup$
    – PDT
    Aug 23, 2020 at 22:13
  • 9
    $\begingroup$ They are all positive integers. They can be created by repeatedly adding $1$. $\endgroup$
    – WhatsUp
    Aug 24, 2020 at 0:23
  • 3
    $\begingroup$ The answer is far more sophisticated. $\endgroup$ Aug 24, 2020 at 0:48

1 Answer 1

1
$\begingroup$

Partial Solution (1):

You can find 8 Pythagorean quadruples, each containing 512, 65537 and 2 of the remaining numbers.

All of the matches

512 34932 55449 65537
512 39321 52428 65537
512 10023 64764 65537
512 1881 65508 65537
512 18009 63012 65537
512 30840 57825 65537
512 27756 59367 65537
512 20148 62361 65537

I found them using some Matlab

a=[34932, 52428, 10023, 1881, 512, 64764, 63012, 57825, 59367, 65508, 30840, 55449, 18009, 65537, 20148, 39321, 62361, 27756];
b=nchoosek(a,3);
c=sum(b.^2,2);
d=a.^2;
s=find(sum(c==d,1));
sort(b(c==d(s),:),2)

$\endgroup$
4
  • $\begingroup$ @klabuster.These are the correct quadruples. Now you can answer the second question which asks how these numbers were created. $\endgroup$ Aug 26, 2020 at 3:13
  • $\begingroup$ After reading your hint, are you sure there are only 8 quadruples? 512, 8160, 65025, 65537 is for example another one. $\endgroup$
    – klabuster_
    Aug 26, 2020 at 9:20
  • $\begingroup$ If found 32 solution that satisfy the conditions of the hint for n=3, there are many for n=4; There are 13 quadrupels with a=65537 and b=512 (b<c<d) $\endgroup$
    – klabuster_
    Aug 26, 2020 at 14:56
  • $\begingroup$ And the second question remains to be answered. $\endgroup$ Aug 26, 2020 at 15:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.