(3) Let A = a + a + a + a +1 where a is a...
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(3) Let A = a¹ + a² + a² + a +1 where a is a positive odd integer such that a = 0 mod 5. Show that: (a) p = 1 mod 10 for any prime divisor p of A. (b) There are infinitely many primes of the form 10k +1 without using the Dirichlet's Theorem on arithmetic progressions. (3) Let A = a¹ + a² + a² + a +1 where a is a positive odd integer such that a = 0 mod 5. Show that: (a) p = 1 mod 10 for any prime divisor p of A. (b) There are infinitely many primes of the form 10k +1 without using the Dirichlet's Theorem on arithmetic progressions.
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To prove the given statements lets first simplify the expression A a a a a 1 Simplifying A we have A a a a a 1 2a a 1 a To show that p 1 mod 10 for an... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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