Thursday, 27 September 2018

independence - root of prime numbers are linearly independent over mathbbQ

How can we prove by mathematical induction that 1,2,3,5,,pn (pn is the nth prime number) are linearly independent over the rational numbers ?



base case (n=1)_: 1,2 are linearly independent over the field Q otherwise a1+b2=02=ab which is absurd.



Then I am stuck.

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