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Fill in the Blanks
If 2515 is divided by 13, the reminder is ______.
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Solution
If 2515 is divided by 13, the remainder is 12.
Explanation: Let 2515 = (26– 1)15
= `""^15"C"_0 (26)^15 (-1)^0 + ""^15"C"_1 (26)^14 (-1)^1 + ""^15"C"_2 (26)^13 (-1)^2 + ... + ""^15"C"_15 (-1)^15`
= `26^15 - 15(26)^14 + .... - 1 - 13 + 13`
= `26^15 - 15 * (26)^14 + ... - 13 + 12`
= `13lambda + 12`
∴ The remainder = 12.
Concept: Proof of Binomial Therom by Combination
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