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2.6 Let f(x) = x² + ax+bZ[x] be a quadratic polynomial with integer coefficients, for example, f(x) = x²+x+6. Formulate a conjecture about when the set {f(n): ne Z and f(n) is prime} is infinite. Give numerical evidence that supports your conjecture.

2.6 Let f(x) = x² + ax+bZ[x] be a quadratic polynomial with integer coefficients, for example, f(x) = x²+x+6. Formulate a conjecture about when the set {f(n): ne Z and f(n) is prime} is infinite. Give numerical evidence that supports your conjecture.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2.6 Let f(x) = x² + ax+b € Z[x] be a quadratic polynomial with integer coefficients, for example, f(x) = x² + x + 6. Formulate a conjecture about when the set {f(n): ne Z and f(n) is prime} is infinite. Give numerical evidence that supports your conjecture.
Transcribed Image Text:2.6 Let f(x) = x² + ax+b € Z[x] be a quadratic polynomial with integer coefficients, for example, f(x) = x² + x + 6. Formulate a conjecture about when the set {f(n): ne Z and f(n) is prime} is infinite. Give numerical evidence that supports your conjecture.
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