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Math Prime number puzzle 15april

Puzzle


If 'a' is a prime number, then prove, that a*a+26 is NOT a prime number (whether it is true).

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Solution:


Showing that a*a+26 is not prime when a=3 is true but not a math. proof. However it is quite easy: (if I didn't misunderstand)
a*a + 26 =
a*a -1 + 27=
(a-1)*(a+1) + 27

Now, since a is prime, it can not be a mutliplier of 3. Then either (a+1) or (a-1) should be a multiplier of 3.
Then (a-1)*(a+1) is multiplier of 3
And (a-1)*(a+1) +27 is also multiplier of 3
Then it's not prime.