One of the major impediments to providing broadband connectivity in semi-urban and rural India is the lack of robust and affordable backhaul. Fiber connectivity in terms of backhaul that is being planned (or provided) by the Government of India would reach only till rural offices (named Gram Panchayat) in the Indian rural areas. In this exposition, we articulate how TV white space can address the challenge in providing broadband connectivity to a billion plus population within India. The villages can form local Wi-Fi clusters. The problem of connecting the Wi-Fi clusters to the optical fiber points can be addressed using a TV white space based backhaul (middle-mile) network.The amount of TV white space present in India is very large when compared with the developed world. Therefore, we discuss a backhaul architecture for rural India, which utilizes TV white spaces. We also showcase results from our TV white space testbed, which support the effectiveness of backhaul by using TV white spaces. Our testbed provides a broadband access network to rural population in thirteen villages.The testbed is deployed over an area of 25km 2 , and extends seamless broadband connectivity from optical fiber locations or Internet gateways to remote (difficult to connect) rural regions. We also discuss standards and TV white space regulations, which are pertinent to the backhaul architecture mentioned above.
It is well known that a polynomial φ(X) ∈ Z[X] of given degree d factors into at most d factors in F p for any prime p. We prove in this paper the existence of infinitely many primes q so that the given polynomial φ(X) splits into exactly d linear factors in F q by using only elementary results in field theory and some elementary number theory by proving that φ splits in F q iff P has a root in F q for all sufficiently large primes q, where P ∈ Z[X] is any polynomial such that P has a root β ∈ C for which Q(β) is the splitting field of φ over Q. Furthermore, we prove that any such P splits in F r iff it has a root in F r , for all sufficiently large primes r. Existence of infinitely many such P for any given φ is also proven.
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