Prove that 7^(2n-1) + 13^(2n-1) is divisible by 10 for all n in N. I know this is done using algebra and followed by the definition of divisibility. I just got a bit lost in the algebra.
The induction step:
Assume that 10 divides $\displaystyle 7^{2n-1}+13^{2n-1}$.
Want to show for n+1, 1.e want to show that 10 divides
$\displaystyle 7^{2(n+1)-1}+13^{2(n+1)-1}=7^{2n+1}+13^{2n+1}=49.7^{2n-1}+169.13^{2n-1}$
Let see if you can go from here............
Here's another one and not sure what to do with the exponents on this... Prove the if 0<a<b then a^(1/n) < b^(1/n) for n in N. Or how to show for n + 1.
Oh nm this would be nth roots so prove by contradiction... sorry I answered my own question..