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I didn`t understand Ramesh sir`s explanation to this the integer next above (√3 +1)2mcontains 2m+1 as a factor. how can we say that?7 years agoAnswers : (1)for m=0, (root3 +1)2m = 1 is an intezerso next intezer is 2, whihc has simply 2 as one factor ( put m=0 in 2(m+1) )for `m` non zerointezer 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)2mwe 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 welcomeregardsRamesh

I didn`t understand Ramesh sir`s explanation to this the integer next above (√3 +1)2mcontains 2m+1 as a factor. how can we say that?7 years agoAnswers : (1)for m=0, (root3 +1)2m = 1 is an intezerso next intezer is 2, whihc has simply 2 as one factor ( put m=0 in 2(m+1)  )for `m` non zerointezer 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)2mwe 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 welcomeregardsRamesh

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Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
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