If 97+79 is divisible by 2". Then find the greatest value of n, where

1.	If 97+79 is divisible by 2". Then find the greatest value of n, where n EN
Answer» We have79+97=−(1−8)9+(1+8)779+97=−(1−8)9+(1+8)7 ⇒−(1−9C1.81+9C2.82−......−9C9.89)+(1+7C1.81+7C2.82+....+7C7.87)⇒−(1−9C1.81+9C2.82−......−9C9.89)+(1+7C1.81+7C2.82+....+7C7.87) ⇒16×8+64[−(9C2−........−9C9.87)(7C2+.....+7C7.85)]⇒16×8+64[−(9C2−........−9C9.87)(7C2+.....+7C7.85)] ⇒64⇒64(an integer)

If 97+79 is divisible by 2". Then find the greatest value of n, where n EN

Answer»

We have79+97=−(1−8)9+(1+8)779+97=−(1−8)9+(1+8)7

⇒−(1−9C1.81+9C2.82−......−9C9.89)+(1+7C1.81+7C2.82+....+7C7.87)⇒−(1−9C1.81+9C2.82−......−9C9.89)+(1+7C1.81+7C2.82+....+7C7.87)

⇒16×8+64[−(9C2−........−9C9.87)(7C2+.....+7C7.85)]⇒16×8+64[−(9C2−........−9C9.87)(7C2+.....+7C7.85)]

⇒64⇒64(an integer)