| The greatest common divisor of \[{{3}^{{{3}^{333}}}}+1\]and \[{{3}^{{{3}^{334}}}}+1\] is [SSC (10+2) 2010] |
A) \[{{3}^{{{3}^{333}}}}+1\]
B) 20
C) 2
D) 1
Correct Answer: D
Solution :
| Given, \[{{3}^{{{3}^{333}}}}+1\] and \[{{3}^{{{3}^{334}}}}+1={{27}^{333}}+1\] |
| and \[{{27}^{334}}+1\] |
| Now \[({{x}^{m}}+{{a}^{m}})\] is divisible by \[(x+a)\]for odd m. |
| \[\therefore \] \[(27+1)\]divides \[({{27}^{333}}+1)\] and does not divide \[({{27}^{334}}+1).\] |
| \[\therefore \] HCF of \[({{27}^{333}}+1)\] and \[({{27}^{334}}+1)\] is 1. |
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