Math Arguments

More Algebra Patterns

\(n \hspace{10mm}2^n+3^n \hspace{10mm} .... Factors \)
\(1 \hspace{10mm}2^1+3^1 = 5 \hspace{10mm} 1,5 \) prime
\(2 \hspace{10mm}2^2+3^2 = 13 \hspace{10mm} 1,13 \) prime
\(3 \hspace{10mm}2^3+3^3 = 35\hspace{10mm} 1,5,7,35 \)
\(4 \hspace{10mm}2^4+3^4 = 97 \hspace{10mm} 1,97 \) prime

Complete the table through \(n=10\)

What do you notice? Is there some pattern? What are you wondering about this pattern?

\(2^n + 3^n\) in general?

\(a^n + b^n \), if a, b, and n are positive integers?