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- Homework Statement
- Prove algebraically that ##n^3+3n-1## is odd for all positive integers ##n##.

- Relevant Equations
- Algebra

This is a past paper question; Find the solution here; Well understood

Now i was just thinking along this lines;

Let ##n=x##,

then ##f(x)=x^3+3x-1##

##f(x) =x(x^2+3)-1##

since ##x∈ℤ^{+}## then ##x(x^2+3)## will always be even implying that ##x(x^2+3)-1## is odd.

Would this approach hold or i have to stick with ms? Thanks.

Now i was just thinking along this lines;

Let ##n=x##,

then ##f(x)=x^3+3x-1##

##f(x) =x(x^2+3)-1##

since ##x∈ℤ^{+}## then ##x(x^2+3)## will always be even implying that ##x(x^2+3)-1## is odd.

Would this approach hold or i have to stick with ms? Thanks.