(3^12 + 2^8)(3^12 - 2^8)
(3^12 + 2^8)(3^6 + 2^4)(3^6 - 2^4)
(3^12 + 2^8)(3^6 + 2^4)(3^3 + 2^2)(3^3 - 2^2)
The final term is 23
The penultimate term is 31
We already have two factors.
Method One to get that 5 is a factor, consider (3^6 + 2^4):
The last digit of powers of 3 ; 3, 9, 7, 1, 3, 9, 7, 1, ...
The last digit of powers of 2 : 2, 4, 8, 6, 2, 4, 8, 6, ...
9 + 6 = 15, so (3^6 + 2^4) ends with 5, so 5 is a factor.
Method Two to get that 5 is a factor, consider (3^6 + 2^4):
It's not too hard to calculate (3^6 + 2^4) as 27^2 = 16 = 745, and dividing that by 5 yields 149 which is prime.
Prime factors include: 5, 23, 31, and 149.
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Posted by Larry
on 2024-08-02 12:25:34 |
No Subject