Question

prove from mathematical induction,
(7^n-3^n) is divisible by 4.

Answer 1

By Induction principle we have if a expression true for n=1,and n=n, and n=n+1,then it is true for all N
This is surely divisible by 4 for n=1
In the second step we assume that the statement is true for n=n,
Now the third step is for n=n+1
the given expression is 7^(n+1)-3^(n+1)

Answer 2

if its divisible by 4 then we can write it as:\[7^n-3^n=4m\]

Answer 3

show its true for n=1 (simple)

Answer 4

assume its true for n=k:\[7^k-3^k=4m\]

Answer 5

then use that to prove its also true for n=k+1

Answer 6

to get:\[7^{k+1}-3^{k+1}=7.7^k-3.3^k=7(4m+3^k)-3.3^k=28m+7.3^k-3.3^k\]\[=28m+4.3^k\]

Answer 7

QED

Answer 8

Shri Krishna Jugtawat - do you understand the steps?

Answer 9

Yeah asnaseer was right with his proof

Answer 10

yes. thank you

Answer 11

yw

Answer 12

in which class do you read asnaseer?

Answer 13

:-) I am well past my "best by date" - I work full time as a software engineer and follow maths as a hobby

Answer 14

where from you are?

Answer 15

I am based in London, UK - what about you - where do you study and where are you based?

Answer 16

i m reading in 11th standered in india. i m littile weak in maths.

Answer 17

I'm sure you'll improve very fast - at least you are making an effort in learning the subject - have faith in your ability and keep it up.