Difference between revisions of "2008 iTest Problems/Problem 4"
m (→See also) |
(→See also) |
||
| Line 6: | Line 6: | ||
We know that any prime number, excluding <math>2</math>, is congruent to <math>1 \pmod 2</math>. Thus, if both of the primes are not <math>2</math>, their difference would be congruent to <math>0 \pmod 2</math>. Because <math>11 \equiv 1 \pmod 2</math>, one of the primes must be <math>2</math>. It follows that the other prime must then be <math>13</math>. Therefore, the sum of the two is <math>13+2=\boxed{15}</math>. | We know that any prime number, excluding <math>2</math>, is congruent to <math>1 \pmod 2</math>. Thus, if both of the primes are not <math>2</math>, their difference would be congruent to <math>0 \pmod 2</math>. Because <math>11 \equiv 1 \pmod 2</math>, one of the primes must be <math>2</math>. It follows that the other prime must then be <math>13</math>. Therefore, the sum of the two is <math>13+2=\boxed{15}</math>. | ||
| − | |||
| − | |||
| − | |||
| − | |||
Revision as of 17:49, 22 January 2017
Problem
The difference between two prime numbers is 
. Find their sum.
Solution
We know that any prime number, excluding 
, is congruent to 
. Thus, if both of the primes are not , their difference would be congruent to 
. Because 
, one of the primes must be . It follows that the other prime must then be 
. Therefore, the sum of the two is 
.
