## Problem

x is a prime number greater than 3. Prove that 2x

^{2}+190 is a multiple of 48.## Answer Submission Is Not Available

Form is valid through January 2017

## Solution

Dear visitors and friends of the site. Thank you for your solutions. Sadly, this time no correct answers have been submitted.

Here is the solution:

Our number is 2(x^{2 }- 1+96) . Then x^{2 }- 1 =(x-1)(x+1).

As x is prime, x-1 and x+1 are even and one of them s a multiple of 4. Hence x^{2 }- 1 is a multiple of 8.

^{2 }- 1 is a multiple of 24 and hence our original expression is a multiple of 48. Thank you again and see you in February. Serge Hazanov
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