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Using binomial theorem, prove that 6^n-5...

Using binomial theorem, prove that `6^n-5n` always leaves he remainder 1 when divided by 25.

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Verified by Experts

Writing `6^{n}=(1+5)^{n}`
We know that
`(a+b)^{n}=n_{C_0} a^{n} b^{0}+n_{C_1} a^{n-1} b^{1}+ldots . .+C_{n} a^{n-n} b^{n}`
Putting `a=1, b=5`
` (6)^{n} =C_{0} 1^{n} 5^{0}+{ }^n_{C_1} 1^{n-1} 5^{1}+C_{2} C^{n-2} 5^{2}+ldots . .+^n_{C_n} 1^{n-n} 5^{n} `
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