1read linear factor as a+b
suppose a,b,n are positive integers , all greater than 1.
if an+bn is Prime then what can be said about n ?
A) n must be 2
B) n need not be 2 but must be a power of 2
C) n need not be a power of 2 but must be even
D) none of the above is necessarily true
Please provide the solution.
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5 Answers
1answer is C or else a^n + b^n is reducible if n is odd, one linear factor being (a-b)
262take counter example as a6 +b6 which has two factors
i think answer should be B) but i have no idea how to prove it.
1seems true. as if n=(2^x).y where y is necessarily a odd integer, i think the above expression can be factorized yielding (a^(2^x)) +b (^(2^y)) as a linear factor.
it should be B
