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Show that if Statement 1 is true then Statement 2 is also true

Source: MTRP 2017 Class 11-Short Answer Type Question: Problem 4 :-

May 26, 2020
algebrapolynomial

Problem Statement

An irreducible polynomial is a not-constant polynomial that cannot be factored into product of two non-constant polynomials. Consider the following statements :- Statement 1 : p(x)p(x) be any monic irreducible polynomial with integer coefficients and degree ≥4\geq 4. Then p(n)p(n) is a prime for at least one natural number nn Statement 2 : n2+1n^2+1 is prime for infinitely many values of natural number nn Show that if Statement 1 is true then Statement 2 is also true
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