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Question
The expression 79 + 97 is divisible by 64.
Options
True
False
Solution
This statement is True.
Explanation:
79 + 97 = (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 × 82 – 36 × 82) + …
= (56 + 72) + (21 – 36)82 + …
= 128 + 64 (21 – 36) + …
= 64[2 + (21 – 36) + …]
Which is divisible by 64
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