Question

Prove by recurrence that 5^2n -14^n is a multiple of 11.

Answer 1

i can show with induction but no idea what recurrence is.

Answer 2

ok thanks :/ well prove that an assumption P(n) is true is to assume first that for n=0 P(0) is true and then prove that if P(n) is true then P(n+1) is also true. Then P(n) is true for any value of n. (sorry if my english is bad !) how would you do it by induction?

Answer 3

induction proves for all n in natural

Answer 4

want me to show?

Answer 5

yes please

Answer 6

sec

Answer 7

I can't really see a nice proof by induction...

Answer 8

its nice enough

Answer 9

sec

Answer 10

Oh, never-mind then...

Answer 11

Damn, I DO like... nice!

Answer 12

So do I ! Big Thanks !!!

Answer 13

np

Answer 14

I guess its the same thing just show that its true for n = 0 and 0 is a multiple of 11 because 0*11 = 0

Answer 15

yeah, sure

Answer 16

nice

and for n=1 its true suppose that\[25^n-14^n=11k\]now u have\[25^{n+1}-14^{n+1}=25\times25^n-14\times14^n+25\times14^n-25\times14^n\] \(=25(25^n-14^n)+11\times14^n=25\times11k+11\times14^n\)