Dear friends and visitors of the site,
this is the April 1st problem:
Prove that for any prime number m > 3, m4 -1 is a multiple of 48.
Answer Submission Is Not Available
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:
m4 -1 = (m -1)(m+1)( m2 +1). m -1, m+1 and m2 +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=48Thank you and try to solve the May problem.