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The expression 7^{9} + 9^{7} is divisible by 64.

#### Options

True

False

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#### Solution

This statement is **True**.

**Explanation:**

7^{9} + 9^{7} = (1 + 8)^{7} – (1 – 8)^{9}

= `[""^7C_0 + ""^7C_1 * 8 + ""^7C_2 (8)^2 + ""^7C_3(8)^3 + ... + ""^7C_7(8)^7] - [""^9C_0 - ""^9C_1 8 + ""^9C_2 (8)^2 - ""^9C_3(8)^3 + ... ""^9C_9(8)^9]`

= (7 × 8 + 9 × 8) + (21 × 8^{2} – 36 × 8^{2}) + …

= (56 + 72) + (21 – 36)8^{2} + …

= 128 + 64 (21 – 36) + …

= 64[2 + (21 – 36) + …]

Which is divisible by 64

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