## Problem

Dear friends and visitors of the site,

this is the April 1st problem:

Prove that for any prime number m > 3, m^{4} -1 is a multiple of 48.

## Answer Submission Is Not Available

Form is valid through April 2018

## Solution

Dear friends and visitors of the site.

Thank you for numerous answers and solutions.

The first to send a correct solution was Jacqueline and we congratulate her!

Here is my solution to the problem:

m^{4} -1 = (m -1)(m+1)( m^{2} +1). m -1, m+1 and m^{2} +1 are even, so it is a multiple of 16 (one of them is a multiple of 4).

Between m-1, m+1 and m one is a multiple of 3, but not m.

Thus 16x3=48

Thank you and try to solve the May problem.Serge Hazanov

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