Question: (3) Let A = a + a + a + a +1 where a is a positive odd integer such that a = 0

$(3) Let ( A=a^{4}+a^{3}+a^{2}+a+1 ) where ( a ) is a positive odd integer such that ( a equiv 0 ) mod 5 . Show that: ($

(3) Let A = a + a + a + 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 full answer

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