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# True or False :The expression $7^9+9^7$ is divisible by $64$.

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array}$

Can you answer this question?

Toolbox:
• $(a+b)^n=nC_0x^n a^0+nC_1x^{n-1} a^1+.......nC_n x^0a^n$
We have $7^9+9^7=-(1-8)^9+(1+8)^7$
$\Rightarrow -(1-9C_1.8^1+9C_2.8^2-......-9C_9.8^9)+(1+7C_1.8^1+7C_2.8^2+....+7C_7 .8^7)$
$\Rightarrow 16\times 8+64[-(9C_2-........-9C_9.8^7)(7C_2+.....+7C_7.8^5)]$
$\Rightarrow 64$ (an integer)
Hence the given statement is True.
answered Jun 25, 2014