Question

Show that 17^8+13^7-5^8+2^7 is divisible by 3

Answer 1

Here's Your answer :-

this statement can be Written as 17^8 -5^8 + 13^7 + 2^7.

for a^n - b^n where n is even then, this is divisible by (a-b) ..& when a^n+b^n where n is odd no. then It is divisible by (a+b)

.

= 17-5 + ( 13+2)

= 12 + 15

= 27 since 27 can be expressed as 3*3*3* . therefore, It is divisible by 3

or, Another method

Answer:

here's your answer

Step-by-step explanation:

17^8 = ( 17 × 1 ) ^8 ... By uniqueness of Fundd

amental thereom. Only 17 & 1 can divide its square, cube...etc to any 17^n ..

similarly , (13^7) = (13•1)^7 ... only 13 & 1 can divide its 13^n...

as we know , Both the nos. are not divisible by 3. let's assume they are in power of degree 1 .

therefore, (17+13) = 30 ..

also, 5^8 Follows same rule.. so only 5 & 1 will divide its 5^n exactly ... & 2^7 .. similarly, 2 &1 will divide its 2^n..

let's simplify -5 + 2 = -3

again,

30-3 = 27 ... & this is what it divisible by 3 .. hence this statement will be division by 3