 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Divisibility of 29 (Posted on 2013-05-15) The integers x,y,z are such that 29 divides the sum x4+y4+z4. Determine if 294 also divides x4+y4+z4.

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 4.0000 (1 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Solutions I can find (partial solution) | Comment 1 of 4
Obvious solutions
x=y=z=0

If x=y=z=29 then the sum is 3*29^4 which is divisible by 29^4.

You can generalize this result to:

(29a)^4 + (29b)^4 + (29c)^4 = 29^4(a^4+b^4+c^4) for any integers a,b,c.

So the answer to the problem is either "sometimes" or "yes, always"

Are there solutions where x,y,z are not all multiples of 29?

 Posted by Jer on 2013-05-15 12:25:00 Please log in:
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