This isn't the difference of power identity

Algebra Level 4

$\large \bigg ( 16^{101}+8^{101}+4^{101}+2^{101}+1 \bigg ) \bmod {(2^{100}+1)} = \ ?$

1 solution

Alex Zhong
Mar 31, 2015

Let $x =2^{100}$ , such that the expression can be rewritten as

$16x^4 + 8x^3 + 4x^2 + 2x +1 \equiv \boxed{11} \pmod {x+1}$ .

Did the very same way!

Swapnil Das - 5 years, 10 months ago

sir why this expression is equal to 11 (mod x+1)

Deepansh Jindal - 4 years, 10 months ago

Hint: Remainder Theorem.

Swapnil Das - 4 years, 10 months ago

thanks sir...

Deepansh Jindal - 4 years, 10 months ago