perplexus.info :: Just Math : QUICKIE X

QUICKIE X (Posted on 2017-03-28)

Let x be a positive integer of the form 24n − 1, where n is an integer.

Prove that if a and b are positive integers such that x = ab,
then a + b is a multiple of 24.

See The Solution Submitted by Ady TZIDON

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re: Solution....hint/spoiler

| Comment 2 of 3 |

(In reply to Solution by broll)

Hint (edited):

n=1 ab=24-1=23=23+1

23+1 =24 , multiple of 24

proceed by induction on n - > adding 24 changes nothing

Edited on August 8, 2017, 3:59 am

Posted by Ady TZIDON on 2017-03-28 14:11:12

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