Is it a prime or not?
Determine whether the number is prime or composite.
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4 solutions
Discussions for this problem are now closed
Moderator note:
Your solution is complete. But it isn't required to show that it has 3 factors nor did you prove that the other factor: couldn't be factored further.
Moderator note:
Although you got the right answer, factorization of a number is much harder to do especially when the number is large and when the factors are unknown. So this method is undesired when there isn't any computational aids.
The given number can be expressed as follows: 4 7 + 6 8 + 3 1 6 = ( 2 2 ) 7 + ( 2 ⋅ 3 ) 8 + ( 3 2 ) 8 . Applying properties of (integer) exponents, we have 4 7 + 6 8 + 3 1 6 = ( 2 7 ) 2 + 2 8 ⋅ 3 8 + ( 3 8 ) 2 . This is equivalent to 4 7 + 6 8 + 3 1 6 = ( 2 7 ) 2 + 2 ⋅ 2 7 ⋅ 3 8 + ( 3 8 ) 2 = ( 2 7 + 3 8 ) 2 . Since we have established that 4 7 + 6 8 + 3 1 6 = ( 2 7 + 3 8 ) 2 , a perfect square number, the number must be composite!