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Using Binomial theorem, prove that 6^(n)...

Using Binomial theorem, prove that `6^(n)-5n` always leaves remainder 1 when divided by 25 for all positive interger n .

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`6^(n)-5n =(1+5)^(n) -5n`
`= (1+5n+.^(n)C_(2).5^(2)+.^(n)C_(3)5^(3)+"…..")-5n`
`= 25(.^(n)C_(2)+.^(n)C_(3)+"……")+1`
Hence, `6^(n) - 5n` when divided by 25 leaves 1 as remainder.
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