#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# determine all positive integers n such that the polynomial with n+1 terms f(x)=(xpower 4n)+xpower 4(n-1)+....+xpower8+(xpower4)+1 is divisible by g(x)=(xpower 2n)+xpower 2(n-1)+....+xpower4+xpower2)+1.

10 years ago

both f(x) and g(x) are geometric progressions. for f(x) and g(x),a=1,for f(x), r=x4, for g(x), it is x2

f(x)/g(x)=((1-x4(n+1))/(1-x4))((1-x2(n+1))/(1-x2))=(1+x2(n+1))/(1+x2), it is clear from algebra that n+1 is odd, implying that n is any even natural number

10 years ago

both the num(numerator) and den(denominator) are simple geometric progressions

num/den= ((1-x4(n+1))/(1-x4))(1-x2)/(1-x2(n+1)) = (1+x2(n+1))/(1+x2)

obviously n+1 is odd which implies that n is any even natural number