Difference between revisions of "2018 AMC 10B Problems/Problem 11"
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==Solution 1== | ==Solution 1== | ||
− | + | Because squares of a non-multiple of 3 is always <math>1\mod 3</math>, the only expression is always a multiple of <math>3</math> is <math>\boxed{\textbf{(C) } p^2+26} </math>. This is excluding when <math>p=3</math>, then <math>p^2+26=35</math> which is still composite. |
Revision as of 15:04, 16 February 2018
Which of the following expressions is never a prime number when is a prime number?
Solution 1
Because squares of a non-multiple of 3 is always , the only expression is always a multiple of
is
. This is excluding when
, then
which is still composite.