A Proof of Infinite PrimesDivyendu Priyadarshi
This paper presents a complete and exhaustive proof that an Infinite Number of Triplet Primes exist. The approach to this proof uses same logic that Euclid used to prove there are an infinite number of prime numbers. Then we prove that if p > 1 and d > 0 are integers, that p and p ...
Proof It is clear that if ‖x‖ < 1/ν for a certain infinite ν, then ‖x‖ < 1/ℕ, for every finite natural number ℕ, because a finite number is always less than an infinite number. So, in order to prove the converse, assume that ‖x‖ < 1/ℕ for every finite natural...
While reading Walter Rudin's Principles of Mathematical Analysis, I ran into the following theorem and proof: Theorem 2.12. Let {En}{En}, n=1,2,…n=1,2,…, be a sequence of countable sets, and put S=⋃n=1∞En.S=⋃n=1∞En. Then SS is countable. Proof. Let every set EnE...
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We study a natural question in the Iwasawa theory of algebraic curves of genus>1. Fix a prime numberp. LetXbe a smooth, projective, geometrically irreducible curve defined over a number fieldKof genusg>1, such that the Jacobian ofXhas good ordinary reduction at the primes abovep. Fix an ...
A Proof that Exists an Infinite Number of Sophie Germain PrimesMarko Jankovic
3) Consequently, and this closes our proof: let's consider the set (whose cardinality is infinite) of monogenic biquadratic number fields: . Then each fθ(X) checks the above properties, this means that for family M, all its fields, do not admit any inert prime numbers p ∈ N. 2020-...
Existence of non-preperiodic algebraic points for a rational self-map of infinite order, ArtículoLet $X$ be a variety defined over a number field and $f$ be a dominant rational self-map of $X$ of infinite order. We show that $X$ admits many algebraic points which are not preperiodic...
Jackson Lawrence Capper