How-to-check-f-g-is-the-smallest-h-I-have-no-idea-Find-the-smallest-positive-integer-n-for-which-the-function-f-n-n-2-n-17-is-composite-Do-the-same-for-the-functions-g-n-n-2-21n-1-and-h

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Question Number 168458 by aaaspots last updated on 11/Apr/22

How to check f g is the smallest h I have no idea Find the smallest positive integer n for which the function f(n) = n^2 + n + 17 is composite. Do the same for the functions g(n) = n^2 + 21n + 1 and h(n) = 3n^2 + 3n + 23

H o w t o c h e c k f g i s t h e s m a l l e s t

h I h a v e n o i d e a

Find the smallest positive integer n for which the function f(n) = n^2 + n + 17 is composite. Do the same for the functions g(n) = n^2 + 21n + 1 and h(n) = 3n^2 + 3n + 23

Commented by Rasheed.Sindhi last updated on 11/Apr/22

f(n)=n^2 +n+17 f(17) is certainly composite: f(17)=17^2 +17+17=17(17+1+1) So the required n≤17 Test for f(1),f(2),...,f(16).They′re all primes. ∴ The smallest n for which f(n) is composite is 17. Don′t know simpler method.

f (n) = n^{2} + n + 17

f (17) i s c e r t a i n l y c o m p o s i t e :

f (17) = 17^{2} + 17 + 17 = 17 (17 + 1 + 1)

S o t h e r e q u i r e d n ⩽ 17

T e s t f o r f (1), f (2), \dots, f (16) . T {h e y}^{'} r e

a l l p r i m e s .

∴ T h e s m a l l e s t n f o r w h i c h f (n) i s

c o m p o s i t e i s 17 .

D {o n}^{'} t k n o w s i m p l e r m e t h o d .

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How-to-check-f-g-is-the-smallest-h-I-have-no-idea-Find-the-smallest-positive-integer-n-for-which-the-function-f-n-n-2-n-17-is-composite-Do-the-same-for-the-functions-g-n-n-2-21n-1-and-h

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