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the integer next above (√3 +1) 2m contains 2 m+1 as a factor. how can we say that?

the integer next above (√3 +1)2m contains 2m+1 as a factor. how can we say that?

Grade:Upto college level

1 Answers

Ramesh V
70 Points
13 years ago

for m=0, (root3 +1)2m = 1 is an intezer

so next intezer is 2, whihc has simply 2 as one factor ( put m=0 in 2(m+1)  )

for 'm' non zero

intezer next to (root3 +1)2m   is (root3 +1)2m + 1 which is less than or equal to (root3 +1)2m + (root3 +1)2m i.e., 2. (root3 +1)2m

we can write 2. (root3 +1)2m  as 2.(4+2(2)1/2)m  which is   =  2m.2. (root3 +2)m   which is divisible by 2(m+1)


any other answers from other experts are welcome

regards

Ramesh


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